阅读说明：本技术 用于提供输出数据组的计算机实现的方法 (Computer-implemented method for providing an output data set ) 是由 B.斯托瓦瑟 于 2020-11-05 设计创作，主要内容包括：一种用于依据通过医学成像方法所确定的输入数据组提供输出数据组的计算机实现的方法,包括步骤：-将用于减少图像噪声的算法(36)应用到输入数据组或依据输入数据组所确定的中间数据组(35),以确定噪声减少的信号数据组(38),-将噪声数据组(39)确定为输入数据组或中间数据组与信号数据组之间的差,-通过将噪声处理算法(41)应用到噪声数据组来确定修改后的噪声数据组(43),和/或通过将信号处理算法(40)应用到信号数据组来确定修改后的信号数据组,以及-通过将修改后的噪声数据组与信号数据组或修改后的信号数据组(42)相加或者通过将噪声数据组与修改后的信号数据组相加来确定输出数据组。(A computer-implemented method for providing an output data set from an input data set determined by a medical imaging method, comprising the steps of: -applying an algorithm (36) for reducing image noise to the input data set or to an intermediate data set (35) determined from the input data set to determine a noise-reduced signal data set (38), -determining a noise data set (39) as a difference between the input data set or the intermediate data set and the signal data set, -determining a modified noise data set (43) by applying a noise processing algorithm (41) to the noise data set and/or determining a modified signal data set by applying a signal processing algorithm (40) to the signal data set, and-determining an output data set by adding the modified noise data set to the signal data set or the modified signal data set (42) or by adding the noise data set to the modified signal data set.)

1. A computer-implemented method of providing an output data set (44, 69, 70) from an input data set (33, 66, 67), the input data set being determined by a medical imaging method, the method comprising the steps of:

-applying an algorithm (36) for reducing image noise to the input data set (33, 66, 67) or to an intermediate data set (35) determined from the input data set (33, 66, 67) to determine a noise-reduced signal data set (38),

-determining the noise data set (39) as a difference between the input data set (33, 66, 67) or the intermediate data set (35) and the signal data set (38),

-determining a modified noise data set (43) by applying a noise processing algorithm (41) to the noise data set (39), and/or determining a modified signal data set (41) by applying a signal processing algorithm (40) to the signal data set (38), and

-determining an output data set (44, 69, 70) by adding the modified noise data set (43) to the signal data set (38) or the modified signal data set (42) or by adding the noise data set (39) to the modified signal data set (44).

2. The computer-implemented method of claim 1,

it is characterized in that the preparation method is characterized in that,

the noise processing algorithm (41) comprises a scaling of the noise data set (39) or a different scaling of different frequency components of the noise data set (39) or a filtering of the noise data set (39).

3. The computer-implemented method of claim 1 or 2,

it is characterized in that the preparation method is characterized in that,

at least one measure (51) for the noise in the input data set (33, 66, 67) or the intermediate data set (35) or the noise data set (39) is determined, wherein the noise processing algorithm (41) depends on the measure (51) for the noise.

4. The computer-implemented method of claims 2 and 3,

it is characterized in that the preparation method is characterized in that,

scaled scaling factors for the noise data set (39) or scaled scaling factors (53) for the frequency components and/or parameters of the filtering are determined as a function of the at least one noise-specific measure (51).

5. The computer-implemented method of any of the above claims,

it is characterized in that the preparation method is characterized in that,

-determining the intermediate data set (35) by applying a variance stabilizing transformation (34) to the input data set (33, 66, 67), wherein the signal processing algorithm (40) is or comprises an associated inverse transformation (45).

6. The computer-implemented method of any of the above claims,

it is characterized in that the preparation method is characterized in that,

in the context of a signal processing algorithm (40), a non-linear function (47), in particular a logarithmic function, is applied to image data of a signal data set (38) or image data of a processing result (46) which is determined from the signal data set (38) in the context of a preprocessing within the signal processing algorithm (40).

7. The computer-implemented method of claim 6,

it is characterized in that the preparation method is characterized in that,

predicting a contribution (48) of scattered radiation occurring when the input data set (33, 66, 67) is acquired to the signal data set (38) or the image data of the processing result (46), wherein the nonlinear function (47) depends on the predicted contribution (48), or wherein the signal data set (38) or the intermediate result (46) is corrected depending on the predicted contribution (48) before applying the nonlinear function (47).

8. The computer-implemented method of any of the above claims,

it is characterized in that the preparation method is characterized in that,

within the scope of the signal processing algorithm (40), a function (50) for contrast matching is applied to image data of a signal data set (38) or to image data of a processing result or of a further processing result (46, 49) which is determined from the signal data set (38) within the scope of a preprocessing within the signal processing algorithm (40).

9. The computer-implemented method of any of the above claims,

it is characterized in that the preparation method is characterized in that,

the signal processing algorithm (40) and/or the noise processing algorithm (41) are parameterized as a function of at least one input parameter and/or at least one output variable (55) of a dose setting (65) used within the scope of the medical imaging method.

10. The computer-implemented method of any of the above claims,

it is characterized in that the preparation method is characterized in that,

an algorithm (36) trained by a machine learning method is used as the algorithm (36) for reducing image noise.

11. A computer-implemented method for data processing in the context of medical subtraction imaging, wherein two input data sets (66, 67) which are respectively determined by a medical imaging method on the same examination object (57) are processed, comprising the steps of:

-applying the computer-implemented method (68) according to any one of claims 1 to 10 to the input data sets (66, 67) in order to determine corresponding output data sets (69, 70),

-the output data sets (69, 70) are subtracted from each other to provide a subtracted data set (71), an

-applying a function (72) for contrast matching to the image data of the subtraction data set (71).

12. A providing device, characterized in that the providing device is designed for performing the computer-implemented method according to any of the preceding claims.

13. A medical imaging apparatus, in particular an X-ray apparatus, comprising a provision apparatus (64) according to claim 12.

14. A computer program for a data processing apparatus having program instructions which, when executed on the data processing apparatus (62), perform the computer-implemented method of any one of claims 1 to 11.

15. A computer-readable data carrier, which comprises a computer program according to claim 14.

Technical Field

The invention relates to a computer-implemented method for providing an output data set from an input data set determined by a medical imaging method. Furthermore, the invention relates to a computer-implemented method for data processing in the context of medical subtraction imaging, a provision device, a medical imaging device, a computer program and a computer-readable data carrier.

Background

In the image data of a medical imaging method, due to various factors (for example, depending on the imaged examination object, the specifically performed examination, the imaging parameters, etc.), significantly different contrasts and noise amplitudes may occur, which may make the analysis of the image data more difficult. This problem may occur in particular in modern methods for dose adjustment, in which the X-ray parameters (i.e. for example tube voltage, tube current, exposure time and aperture parameters and/or focus parameters) are adjusted in dependence on the contrast-to-noise ratio for a particular object. In this case, for example, the water equivalent, the size of the object in relation to the spatial frequency, the measurement speed and the material of the object can be taken into account as additional parameters.

Although the radiation load on the examination object can be reduced by the procedure described. However, the image noise (which depends in particular on the dose) and the object contrast (which depends in particular on the tube voltage) are no longer constant but vary, for example, with a change in the water equivalent. Here, water equivalent represents a parameter of dose adjustment related to the thickness of the patient and can be understood as a measure for an equivalent water layer. The image noise in the image additionally depends on the dose distribution on the detector, wherein very large differences may occur locally.

From the user's point of view, constant noise is desired not only inside the image (i.e. not only in areas where the absorption rate is low but also in areas where the absorption rate is high), but also between different images, e.g. in images of different patients or images for different angles. In some cases, it is also desirable to perform contrast matching in order to achieve the same contrast at the same object thickness of the same material, which makes the analysis of the image data easier.

In principle, it is known in the prior art to reduce image noise, in particular by filtering. For example, spatial frequency filtering or high frequency temporal filtering may be performed by a low-pass filter or a gaussian kernel (Gau β kernel).

Different methods for reducing noise in X-ray images are discussed, for example, in the publication "A composition of denoising methods for X-ray fluoroscopic images" by CERCIELLO, T.et al, Biomedical Signal Processing and Control, 2012, volume 7, page 550-. Here, in order to reduce noise, two kinds of algorithms are used. One for suppressing signal-dependent noise and the other for canceling signal-independent noise. Here, it has been determined that algorithms for removing signal-dependent noise provide better results overall.

The publication "tailored noise models and reactive noise reduction" in Signal Processing, 2009, vol 89, No.12, page 2609, FOI 2639, publication "Clipped noise images: heteroscedastic modeling and practical noise reduction" teaches a two-stage method for noise reduction. Here, a variance stabilizing transformation is first applied to the image data, and then a filter is used for noise independent of the signal in order to perform noise suppression. An inverse transform is then performed to remove the variance stabilization.

However, noise reduction is set to a narrow limit, because too strong noise reduction may result in unnatural image look and may distort image data or generate artifacts. This can make subsequent diagnosis more difficult.

It is more difficult that each contrast match (e.g. to compensate for contrast changes due to dose adjustments) results in a change in the noise spectrum, which places a narrow limit on providing a similar image look and feel for images that have been recorded with dose adjustments, especially at different patients or for different angles. Thus, in order to avoid a strongly varying image impression within one image or when comparing different images, it may be necessary to limit the dose adjustment, so that it is not possible in all cases to use the dose adjustment that is actually most effective for a particular imaging task.

Disclosure of Invention

The object of the present invention is therefore to provide an improved method for processing image data of a medical imaging method, in particular with respect to pure noise reduction, which enables a more similar image impression in an observer even in the case of strongly varying imaging parameters.

According to the invention, this object is achieved by a computer-implemented method for providing an output data set from an input data set determined by a medical imaging method, comprising the steps of:

applying an algorithm for reducing image noise to the input data set or to an intermediate data set determined from the input data set to determine a noise-reduced signal data set,

-determining the noise data set as a difference between the input data set or the intermediate data set and the signal data set,

-determining a modified noise data set by applying a noise processing algorithm to the noise data set and/or determining a modified signal data set by applying a signal processing algorithm to the signal data set, and

-determining an output data set by adding the modified noise data set to the signal data set or the modified signal data set or by adding the noise data set to the modified signal data set.

The invention is based on the following ideas: the noise component and the signal component of the input data set or of the intermediate data set determined from the input data set by the preprocessing are processed separately and, after the separate processing, are combined again. This makes it possible to vary the signal data set and thus in particular the contrast, on the one hand, and the signal noise, on the other hand, at least approximately independently of one another, so that despite the additional degree of freedom for dose adjustment, the desired image impression can be obtained in greater detail or can continue to be achieved.

The desired image impression, i.e. for example the intensity of the noise, the spectral composition of the noise, the contrast present in the image, etc., can be predefined in a fixed manner or can be set according to the preferences of a specific user, for example a physician performing the analysis. The method according to the invention thus supports the analyst in the analysis of the image data of the medical imaging method on the one hand, since, for example, a more uniform image impression within the image and/or a better comparability of different images, which have been recorded, for example, for different examination objects or from different angles, can be achieved. At the same time, on the other hand, the load on the examination subject can potentially be reduced, since it is also possible to allow a dose adjustment which would lead to an excessively inhomogeneous image impression without using the method according to the invention and would thus make meaningful analysis of the image data impossible or at least strongly more difficult.

The signal processing period and/or noise processing algorithm may depend on the specific parameters of the imaging. On the one hand, it may depend on object parameters of the examination object, for example on the weight and/or water equivalent and/or size of the examination object. Additionally or alternatively, it may depend on the output variables of the dose setting or imaging parameters, i.e. for example on the tube voltage, the tube current, the exposure time and/or the aperture setting and/or the focus setting.

The input data may be, in particular, X-ray images, which may be recorded, for example, by means of a flat panel detector. The input data set may describe two-dimensional or three-dimensional image data. In the following, X-ray imaging is exemplarily discussed mainly as a medical imaging method, since the method according to the invention can be used particularly advantageously in conjunction with the dose setting used. In principle, however, the method according to the invention may also be suitably used in other fields of medical imaging, i.e. for example for magnetic resonance tomography data, positron emission tomography data, etc. In the context of X-ray imaging, the method according to the invention can be used for processing two-dimensional image data. In principle, it can also be individual projection images of the computer tomography, which are combined to form a three-dimensional image representation.

In a particularly advantageous variant of the method according to the invention, an input data set is processed, which input data set comprises a plurality of sequentially recorded image data sets. This enables an algorithm for reducing image noise to process a plurality of these image data sets together, for example to perform temporal filtering and thus to suppress temporally high-frequency noise, for example by means of a temporal low-pass filter or gaussian filter. The algorithm for reducing image noise can in particular perform the filtering of the spatial frequencies, for example with a low-pass filter or a gaussian kernel, independently of whether the input data set comprises a plurality of sequentially recorded image data sets. In order to reduce image noise, algorithms known per se, such as those mentioned in the publications mentioned at the outset, can be used. However, as will also be explained later, the algorithm may also be trained by machine learning methods.

The noise processing algorithm may include scaling of the noise data set or different scaling of different frequency components of the noise data set or filtering of the noise data set. By the measures mentioned, a uniform, desired image impression can be set with regard to noise. By changing the frequency composition of the noise with different scaling or filtering of different frequency components, noise shaping is achieved, whereby e.g. a desired coloration of the noise or a de-coloration of the noise may be achieved.

As described above, if the input data set comprises a plurality of sequentially acquired image data sets, the scaling of the different frequency components or the filtering of the noise data set may be related to the time-frequency composition of the noise. Independently of this, the composition of the noise data set can also be varied in terms of spatial frequency by corresponding filtering or scaling of different frequency components of the spatial frequency.

Different scaling of different frequency components may be achieved, for example, by taking a fourier transform of the noise data set and then multiplying by the envelope in frequency space. Alternatively, the inverse envelope is transformed back into position space and convolution is performed there. It may be more efficient, however, to construct the gaussian-laplacian pyramid by applying different sized gaussian kernels and forming differences between the resulting data, with the various layers corresponding to different frequency components.

The scaling factor or a different scaling factor or a filter parameter for the filtering can be fixedly predefined or can also be set by the user or a service technician. Advantageously, however, these variables can depend on the above-mentioned parameters of the imaging, or particularly advantageously on the image data itself of the input data set, as will also be explained in more detail later on.

At least one measure for the noise in the input data set or the intermediate data set or the noise data set may be determined, wherein the noise processing algorithm depends on the measure for the noise. Within the scope of the method according to the invention, the noise should be set in particular to a predetermined target impression. It is therefore advantageous to quantize the noise and then modify it so that the desired characteristics of the noise are achieved.

If substantially only noise is present in the observed data set (this can be achieved in particular for noisy data sets), the amplitude of the image data or, for example, also the standard deviation of the image data can be taken into account as a measure for the noise.

However, if the image data analyzed comprise both signal and noise components, for example if the input data set or the (in particular variance-stabilized) intermediate data set is analyzed directly, it is advantageous to try to separate the signal components at least as far as possible within the scope of the determination of the measure for the noise. For this purpose, for example, a histogram of the image data may be analyzed, and only values lying within a predetermined range may be taken into account, for example, on the basis of the center of gravity or the maximum value of the histogram. The predetermined range can be predefined, for example, as a function of a standard deviation, which can likewise be determined from a histogram or from the image data. For example, all values whose distance from the center of gravity or the maximum of the histogram corresponds maximally to five times the standard deviation can be considered. If for such values, for example, the standard deviation of the distance from the center of gravity or from the maximum is calculated, or a further measure for this deviation, in particular a norm, is also calculated, this represents a good measure for the noise in the image data record observed, as has been derived by preliminary experiments.

In particular, a measure for the noise may be taken into account in order to parameterize the scaling, the frequency-dependent scaling or the filtering. The scaling factor for the scaling of the noise data set or the scaling factor for the scaling of the frequency components and/or the parameters of the filtering may be determined in dependence on at least one measure for the noise.

This enables, for example, the amplitude of the noise or the individual frequency components of the noise to be set to desired values, so that a desired image impression can be achieved in terms of noise. If a plurality of frequency components are parametrically filtered or scaled, a plurality of measures for noise can be determined, wherein in particular separate measures are calculated for different frequency components of the noise. Alternatively, the frequency distribution of the noise may also be considered differently, for example, by determining the color of the noise in addition to the intensity of the noise. The color of the noise may then be compensated by a corresponding filtering or weighting of the frequency components, or a desired coloration may be set.

The relation between the one or more noise-specific measures and the one or more scaling factors or parameters of the filtering may be defined by a predetermined relation, e.g. by a Look-up-table (Look-up-table) or an objective function. In particular, the relationship can be predefined such that at least one measure for the noise in the noise data set is set at least approximately to a predetermined value. The relation, in particular the look-up table, may take into account additional parameters, for example in order to take into account parameters of the X-ray imaging, parameters or user settings of the examination object and/or user preferences. For example, the water equivalent for the patient or the impression of the image selectable by the user may additionally be taken into account.

By applying a variance stabilizing transformation to the input data, an intermediate data set may be determined, wherein the signal processing algorithm is or comprises an associated inverse transformation. In this case, it is possible in particular that no inverse transformation is carried out on the noise data set, as a result of which the noise in the output data set can in particular remain substantially independent of the signal amplitude.

As already explained at the outset, in X-ray imaging a distinction should be made between signal-independent noise, which is caused in particular by noise of the measurement electronics, and signal-dependent noise, which occurs as a result of the quantum behavior of the incident photons. In most cases, noise components, in particular poisson distributions, which depend on the signal dominate. By applying a variance stabilizing Transformation (e.g., variance invariant Transformation Anscombe-Transformation) or also by applying a square root to the image data, the signal dependence of noise can be at least approximately eliminated and the signal independence of noise can be achieved.

On the one hand, this enables algorithms for reducing image noise to be designed to reduce signal independent noise. A large number of known algorithms can thereby be applied, and also potentially new algorithms trained, for example, by machine learning, can be built more simply. At the same time, it is thereby possible to achieve signal-independent noise in the noisy data record and thus ultimately also in the output data record, which is generally regarded as more favorable by the analyst of the respective data record or makes the analysis easier. In particular, distinct noise imaging in regions with strong and low absorption is thereby avoided.

By applying the inverse transformation within the scope of the signal processing algorithm, it is achieved that the modified signal data set and thus also the output data set are not distorted in terms of signal by the variance stabilizing transformation. In principle, variance stabilizing transforms and inverse transforms are known and therefore should not be elaborated upon in detail. For example, reference is made in this respect to the publication of a.foi already cited at the outset.

In particular, the signal processing algorithm may comprise a grey scale transformation. In particular, within the scope of the signal processing algorithm, a nonlinear function, in particular a logarithmic function, can be applied to the image data of the signal data set or to the image data of the processing result, which is determined from the signal data set within the scope of the preprocessing within the signal processing algorithm. The pre-processing may be, for example, the inverse transform described above for the variance stabilizing transform.

Applying a logarithmic function is suitable because hereby the same object thickness difference under the same material in the object under examination results in the same contrast difference based on the exponential decay law in X-ray imaging. This greatly facilitates the analysis of the image data. However, in certain cases, for example for particularly low or particularly high intensities, it may also be advantageous to deviate from the logarithmic function. Furthermore, as will be explained later, scattered radiation correction may be performed.

The non-linear function may be predefined as a look-up table, for example, or may also be predefined as an analytical function. Furthermore, the non-linear function may depend on further parameters. For example, dose setting or, in general, parameters of the X-ray imaging, parameters of the examination object or user-side settings can be taken into account.

Advantageously, a contribution of scattered radiation occurring during the acquisition of the input data set to the signal data set or the image data of the processing result is predicted, wherein the non-linear function depends on the predicted contribution, or wherein the signal data set or the intermediate result is corrected in dependence on the predicted contribution before the application of the non-linear function. This contribution may be in particular an offset which is subtracted or used from the signal data set or from the processing result in order to modify the non-linear function before applying the non-linear function.

The consideration of scattered radiation is particularly important when the method according to the invention is used to generate image data which should be compared directly with one another, or when three-dimensional image data should be reconstructed from two-dimensional image data of an output data set or of a plurality of output data sets. Since different contributions of scattered radiation and thus, for example, different offsets potentially occur in a plurality of images, artifacts may form in the reconstruction of the three-dimensional image data or a comparison of the two-dimensional or three-dimensional image data sets may be made difficult. It may also be advantageous to take scattered radiation into account if the method is applied to only one image data set, since, for example, better comparability of different examinations may be achieved.

In principle, the prediction of the contribution of scattered radiation is known in the prior art and should not be elaborated upon in detail. In particular, the scattered radiation that occurs depends on the patient characteristics, which can be taken into account according to a detailed patient model or also by means of one or more individual parameters, for example the water equivalent or the weight. Furthermore, imaging parameters, i.e. in particular dose adjustment parameters, are relevant. The corresponding relationship may be determined by preliminary experiments and collected, for example, statistically. These relationships may then be saved, for example, in a look-up table, or a functional relationship between the parameter under consideration and the scattered radiation expected to occur or the contribution made therefrom to the image data may be determined, for example, by regression analysis.

In the context of a signal processing algorithm, the function for contrast adaptation can be applied to the image data of the signal data set or to the image data of the processing result or of a further processing result, which is determined from the signal data set in the context of a preprocessing within the signal processing algorithm. Here, the processing result may be a result of applying a nonlinear function or an inverse transform to the signal data group. The further processing result can in particular be processed further if both the inverse transformation and the nonlinear function have been previously applied to the signal data set.

Methods for contrast matching in image data records are known in principle from the prior art, so that only a few examples are briefly discussed below. In the method according to the invention, the significant difference to the conventional method is that contrast adaptation takes place within the scope of the signal processing algorithm and therefore essentially independently of the noise component of the input data set. By subsequently adding the noise data set or the modified noise data set, it is achieved that the noise component of the output data set is at least approximately independent of the contrast matching, whereby the following advantages are achieved over the usual methods: contrast matching does not result in shaping or staining of noise, which may interfere with or distort the image look and feel.

The function for contrast adaptation may comprise a grey scale transformation and/or different frequency components weighted differently in intensity for the signal data set or the processing result or further processing results. For example, high frequency components may be emphasized or suppressed in order to highlight or suppress fine structures.

The function for contrast matching may be fixedly predefined, however, it may preferably depend on parameters of the imaging, in particular on parameters used in the context of X-ray imaging (such as tube voltage, tube current, exposure time and/or settings for aperture or focus). Additionally or alternatively, the function for contrast matching may depend on user settings in order to match the contrast to the desires of the user, in particular of the image analyst. Parameters relating to the examination object, such as the water equivalent, the image content of the processed data record and/or the examination type, can also be taken into account in order to predefine or parameterize the function.

In the method according to the invention, the signal processing algorithm and/or the noise processing algorithm can be parameterized as a function of at least one input parameter and/or at least one output parameter of the dose setting used in the context of the medical imaging method. The input parameters or output parameters can be provided directly by the imaging device. This may be advantageous, for example, if a computer-implemented method should be used already in the scope of the first screening of the measured data or the direct analysis. However, it is also possible to store the at least one input variable or the at least one output variable together with the input data set, for example in an image database, or to provide it in another way together with the input data set for processing by means of a computer-implemented method. In this case, the computer-implemented method may therefore also be carried out separately from the measurement data acquisition, for example also on a separate device or by a further service provider.

The input parameters for dose setting can be, in particular, parameters of the examination subject, i.e. for example parameters of the patient (such as water equivalent, weight, size, etc.). Additionally or alternatively, measurement data acquired during the acquisition of the input data set may be taken into account, for example the currently acquired dose, the contrast and/or the image noise, in particular the contrast-to-noise ratio for a specific object, etc.

For example, tube current, tube voltage, exposure time and/or filter settings, aperture settings and/or focus settings can be considered as output variables.

Different parameters of the noise processing algorithm or the signal processing algorithm or the processing steps that can be performed within the scope of these algorithms have been set forth before.

An algorithm trained by a machine learning method may be used as an algorithm for reducing image noise. Such algorithms may be or include, for example, neural networks, support vector machines, decision trees, and/or bayesian networks. Alternatively or additionally, the trained algorithm may also be based on a k-means algorithm, Q learning, genetic algorithm, and/or association rules. The neural network may be, inter alia, a deep neural network, a convolutional neural network or a convolutional deep neural network. Additionally or alternatively, the neural network may be a competing network, a deep competing network, and/or a generative competing network.

The algorithm may be trained by supervised learning, partially supervised learning, reinforcement learning, active learning, and/or unsupervised learning.

For example, the algorithm may be trained using a training data set comprising a first image data set and a second image data set, respectively, which have preferably been acquired with the same acquisition parameters on the same examination object. For training the algorithm, a cost function can be minimized, which depends on the difference between the measure for the noise in the first image data set and the measure for the noise in the sum data set, wherein the sum data set is determined by applying the algorithm to be trained to the second image data set and adding the resulting data set formed to the first image data set. The minimization of the cost function can be carried out by changing the parameters of the algorithm to be trained, for which purpose, for example, error feedback known per se can be used.

The described method for training an algorithm for reducing image noise exploits the fact that: the image noise in different images is independent of each other, so the variances caused by the noise add up at least approximately. If it is achieved that the measure for the noise in the sum image (e.g. the variance) is the same as the measure for the noise in the first image data set, this indicates that the application of the algorithm has substantially completely eliminated the noise in the second image data set.

Although the training of the algorithm may in principle be part of the method according to the invention, it is particularly preferred in the method according to the invention to use an algorithm for reducing image noise which has been trained before the method according to the invention is started. The invention therefore also relates to a method for training an algorithm for reducing image noise. The invention further relates to a training device designed to carry out the method, to a program for carrying out the steps of the method when the program is executed on a data processing device, and to a computer-readable data carrier storing such a program. The invention further relates to a trained algorithm or a parameter data set for reducing image noise, which parameterizes a predetermined algorithm for providing the algorithm, or to a computer-readable data carrier, which stores the algorithm or the parameters of the algorithm. In particular, as a result of the stated training method, an algorithm or parameters of an algorithm and thus also a data carrier can be provided.

In addition to the computer-implemented method for providing the output data record, the invention also relates to a computer-implemented method for data processing in the context of medical subtraction imaging, wherein two input data records, each determined by a medical imaging method on the same examination subject, are processed. The method comprises the following steps:

applying the computer-implemented method for providing an output data set according to the invention to an input data set in order to determine a corresponding output data set,

-the output data sets are subtracted from each other to provide a subtracted data set, an

-applying the function for contrast matching to the image data of the subtraction data set.

In other words, the method according to the invention for providing an output data set is applied separately to the input data sets before the subtraction of the input data sets, in which method the noise data set and the signal data set are processed separately. After subtraction, contrast matching is performed. In particular, in the context of the preprocessing of the input data set, i.e. in the context of the signal processing algorithm, initially no contrast matching may take place, since this may potentially lead to shifts or the like in the region of interest when determining the subtraction data set. For example, in the context of signal data processing, if variance stabilization has previously been performed, only the inverse transform may be applied initially, and optionally a non-linear function, such as a logarithmic function, may be applied.

The subsequent contrast matching of the image data of the subtraction data set can take place in the same way as has already been explained above in the context of signal data processing with regard to contrast matching and/or is dependent on the parameters mentioned in this respect. By moving the contrast matching to a later point in time of the processing, at which point the noise data set or the modified noise data set and the signal data set or the modified signal data set have been combined again, the contrast matching affects not only the signal component but also the noise component of the image data. However, this may be acceptable if only relatively mild contrast matching is performed. By moving the changed part of the signal component into the signal processing algorithm, in particular into the signal processing algorithm applying the logarithm (by applying the logarithm to significantly change the signal component), it is still possible to achieve a smaller influence on the noise component than in the case of consecutively jointly processing the noise component and the signal component.

In addition to the described computer-implemented method, the invention also relates to a provision device which is designed to carry out the computer-implemented method according to the invention for providing an output data set and/or the computer-implemented method for data processing in the context of medical subtraction imaging. In particular, the provision device may comprise an input interface for receiving one or more input data sets and an output interface for outputting the output data set or the contrast-matched subtraction data set. The provision means can be constructed as data processing means which are designed to carry out the data processing set forth for the method. For example, the data processing can be carried out by a correspondingly programmed processor (for example, a microprocessor, microcontroller, FPGA, DSP, etc.), or else the data processing can be carried out in a distributed manner by a plurality of processors (for example, via the cloud).

The features set forth for the computer-implemented method according to the invention may be transferred to the providing device according to the invention together with the advantages mentioned and vice versa.

Furthermore, the invention relates to a medical imaging apparatus, in particular an X-ray apparatus, comprising a provision apparatus according to the invention. This makes it possible, in particular, to reprocess the input data set or sets by the computer-implemented method according to the invention directly during or following the acquisition, i.e. already during the first visualization for the operator, for example. However, as an alternative to integration into the medical imaging apparatus, the provision apparatus may also be a separate apparatus which obtains input data and/or outputs output data, for example via a network, a database or, in particular, a replaceable data carrier.

Furthermore, the invention relates to a computer program for a data processing device, having program instructions which, when executed on the data processing device, carry out a computer-implemented method according to the invention for providing an output data set and/or a computer-implemented method according to the invention for data processing in the context of medical subtraction imaging.

Furthermore, the invention relates to a computer-readable data carrier comprising a computer program according to the invention.

Drawings

Further advantages and details of the invention emerge from the following examples and the associated figures. Here schematically:

FIG. 1 shows a flow diagram of an embodiment of a computer-implemented method for providing an output data set according to the invention;

FIG. 2 illustrates an algorithm and a data structure used within the scope of the method illustrated in FIG. 1;

FIG. 3 shows the interaction of an embodiment of a providing apparatus according to the invention with a medical imaging apparatus;

FIG. 4 shows algorithms and data structures used within the scope of an embodiment of a computer-implemented method for data processing within the scope of medical subtraction imaging according to the invention;

FIG. 5 illustrates an embodiment of a training method for training an algorithm for reducing image noise by a machine learning method, which may be used within the scope of the computer-implemented method according to the present invention; and

fig. 6 and 7 show exemplary structures of algorithms that may be trained to reduce image noise.

Detailed Description

Fig. 1 shows a flow diagram of a computer-implemented method for providing an output data set from an input data set determined by a medical imaging method. The method is explained below with additional reference to fig. 2, fig. 2 schematically showing algorithms and data structures used within the scope of the method. For the sake of clarity, the two-dimensional individual image data records are each represented as input data records or processing results. However, the described method is also suitable for processing three-dimensional image data sets. It is also possible that the input data set comprises a plurality of image data sets recorded in chronological succession, so that the processing result can also correspondingly comprise a plurality of image data sets. This is also not shown for clarity.

In step S1, an input data record 33 is first provided, which has been determined by a medical imaging method, in particular as an X-ray recording, for example with a flat panel detector. In particular, the acquisition of image data of the input data set can be carried out in an upstream step independently of the computer-implemented method set forth. However, in principle, the acquisition can also be integrated into the method.

In step S2, the variance stabilizing transformation 34 is applied to the input data set 33 to generate the intermediate data set 35. The variance stabilizing transformation 34 is used to modify the noise component of the input data set such that the noise is substantially independent of the measurement signal, i.e. for example to convert the noise from a poisson distribution to a gaussian distribution. For variance stabilization, different methods known per se can be used. For example, a root function or variance invariant transform may be applied to the image data of the input data set 33.

In step S3, the algorithm 36 for reducing image noise is applied to the intermediate data set 35 to determine the noise reduced signal data set 38. Any algorithm 36 suitable for reducing signal independent noise may be used based on the variance stabilization upstream. As will also be explained later, the algorithm 36 may be trained, in particular, by machine learning. To this end, the algorithm 36 may have a large number of free parameters 37 learned within a training range. Subsequently, one possibility for training such an algorithm 36 is set forth also with reference to fig. 5, and subsequently possible structures for the corresponding algorithm are set forth also with reference to fig. 6 and 7.

In step S4, the noise data set is determined by subtracting the signal data set 38 from the intermediate data set 35. The noisy data set essentially represents noise in the intermediate data set 35 or variance stabilized noise in the input data set 33.

Subsequently, the noise data set 39 is processed in parallel by the noise processing algorithm 41 in step S5 and the signal data set 38 is processed in steps S6 and S7, wherein the noise data set 39 is processed by the noise processing algorithm 41 in step S5 to provide a modified noise data set 43 and the signal data set 38 is processed in steps S6 and S7 to provide a modified signal data set 42. In step S8, the modified signal data set 42 is then added to the modified noise data set 43 to provide the output data set 44.

By applying the noise processing algorithm 41 in step S5, the scaling or shaping of the noise should preferably be done such that the actual noise spectrum approximates the desired noise spectrum. In the simplest case, the entire noise data set can be scaled. Preferably, however, different frequency components of the noise data set 7 are scaled differently or the noise data set 39 is filtered in order to adapt the noise spectrum to the desired shape. For example, staining of noise due to the measurement electronics used, etc. may be eliminated.

In this example, for this purpose, different scaling factors 53 are used for the scaling of the frequency components. The division of the noisy data set 39 into frequency components may be achieved, for example, via a fourier transform or by constructing a gaussian-Laplace pyramid (Gau β -Laplace pyramid) in which different sized gaussian filters are applied at different locations, after which the differences between adjacent locations correspond to different frequency components.

For matching the noise, at least one measure 51 for the noise is preferably determined in the intermediate data set 35 or alternatively also in the input data set 33 or in the noise data set 39. For example, the noise amplitude may be determined for different frequency components. Methods for determining such metrics 51 have been discussed in the summary of the invention section of the specification.

Additionally, the scaling factor 53 or further parameters parameterizing the noise processing algorithm 41 may depend on additional information 52, which may relate to, for example, a user-defined function for noise matching, a water equivalent for the examination object or further parameters relating to the imaging or the analysis of the image data, and which have already been discussed above. The scaling factor 53 or the parameters of the noise processing algorithm 41 may be retrieved from a look-up table, for example, depending on the mentioned parameters.

In step S6, the inverse transform 45 for the variance stabilizing transform 34 is first performed within the scope of the signal processing algorithm 40. The variance stabilizing transformation 34 achieves that the noise in the intermediate data set 35 is substantially frequency independent. Here, however, the variance stabilizing transformation distorts the signal components. This is compensated for by applying an inverse transform 45, for which intermediate results 46 substantially correspond to the signal components of the input data set 33.

In an alternative embodiment, steps S2 and S6, i.e., variance stabilizing transformation 34 and inverse transformation 45, may also be omitted. In this case, instead of the intermediate data set 35, the input data sets 33 will be used, respectively; and instead of the intermediate result 46, the processing in step S7 will directly process the signal data set 38.

In step S7, the intermediate result 46 is subjected to contrast processing, or if variance stabilization is omitted, the signal data group 38 is subjected to contrast processing. Here, for example, gradation conversion and spatial frequency operation may be applied. For example, look-up tables, band pass filters, multi-scalar filters, etc. may be used. In the example shown, the application of the non-linear function 47 is performed in sequence in order to determine a further intermediate result 49, and then the function 50 for contrast matching is applied to the further intermediate result 49 in order to determine the modified signal data set 42.

In particular, the non-linear function 47 is modified in dependence on the predicted contribution 48 of scattered radiation to the image data of the signal data set 38 or the processing result 46. This serves in particular to compensate for a shift in the signal data record 38 or the intermediate result 46 due to these scattered radiation. Alternatively, the intermediate result 46 may also be modified before applying the non-linear function 15. The application of a non-linear function, in particular a logarithmic function, may be used to ensure that the same thickness difference of the imaged object under the same material always results in the same contrast change, which may significantly make the analysis of the image data easier.

The function 50 for contrast adaptation may be dependent, in particular, on a parameter 54, which may be dependent, for example, on a dose-adjusted output variable 55 used in the context of a medical imaging method. For determining the parameters 54, for example, a look-up table, a predetermined functional relationship, or the like may be used.

In particular, the function 50 may weight different frequency components in the further intermediate results differently, for example to emphasize fine structures or the like.

In the example discussed with reference to fig. 1 and 2, both the signal data set 38 and the noise data set 39 are modified before being added to the output data set 44. In principle, it is also possible to modify only one of these data sets, leaving the other unchanged.

Fig. 3 shows a medical imaging apparatus 56, in particular an X-ray apparatus, by means of which an input data set 33 can be acquired, which images an examination object 57 in the previously explained method. The control device 58 controls the operation of the imaging device 56. In particular, the control device 58 can carry out a dose adjustment 65, which dose adjustment 65 controls the X-ray dose incident on the examination object 57 as a function of the acquired measurement data, in particular as a function of the contrast-to-noise ratio for the defined object.

The control device 58 can in principle directly supply the determined input data set to an evaluation device 60, for example a workstation computer, for example via a network 59. In this case, however, there may be significant differences in the contrast present or noise present for different examination objects, different angle angles, etc., in particular due to the dose adjustment 65 used, so that the analysis of the image data can be made significantly more difficult.

The acquired input data set 33 is therefore first transmitted to a provision device 61, which implements the method explained above with reference to fig. 1 and 2. This can be achieved, for example, by a corresponding programming of the data processing device 62 by a corresponding computer program. The formed output data set 44 can then be supplied, for example, to an evaluation device 60.

The input data set 33 or the output data set 44 can also be stored temporarily in the database 63 in the first place, so that the described data processing can be carried out independently of the acquisition of measurement data by the medical imaging device 56. In general, if the operating parameters of the medical imaging device 56, in particular the parameters of the dose setting 65, are taken into account, as described above, these parameters can be stored in the database 63 together with the input data set 33.

The illustrated use of a provision device 61, which is constructed separately from the medical imaging device 56, enables, for example, the provision of the method explained as a service. In some cases, however, it may also be advantageous to use, instead of a separate provision device 61, a provision device 64 integrated into the medical imaging device 56, which may be realized, for example, by the control device 58. This enables the advantages of using the method set forth to be achieved independently of external devices.

Fig. 4 shows an embodiment of a computer-implemented method for data processing in the context of medical subtraction imaging. In this case, the two input data records 66, 67 are each processed by the method 68 already described with reference to fig. 1 and 2 to provide a corresponding output data record 69, 70. Subsequently, the output data sets 69, 70 are subtracted from one another in order to provide a subtraction data set 71. Subsequently, the function 72 for contrast matching is applied to the image data of the subtraction data set 71 in order to provide a contrast-matched subtraction data set 73.

In method 68, in contrast to the variant shown in fig. 2, preferably in step S7 no function 50 for contrast matching is applied, but instead a function 72 for contrast matching is used, which function 72 for contrast matching is applied only after the output data sets 69, 70 have been subtracted from one another. This prevents distortion of the subtraction data set 71 due to the different influence of the function 50 on the output data sets 69, 70. Here, it is acceptable that, in the embodiment shown in fig. 4, the function 72 for contrast matching also changes the noise component of the subtraction image 71 together in the range of contrast matching.

In addition to using the function 72 for contrast matching at different points in time in the method, the function for contrast matching may also correspond to the function 50 for contrast matching already discussed with reference to fig. 2. Correspondingly, as already explained for fig. 2 and function 50, the parameters of function 72 may also be varied depending on the imaging parameters or further parameters.

Fig. 5 shows an exemplary training method for training the algorithm 36 for reducing image noise by a machine learning method, which may be used within the scope of the computer-implemented method according to the invention. For training the algorithm, a training data set 74 is used, which comprises a first and a second image data set 75, 76, respectively. Image data sets 75, 76 have been acquired with the same acquisition parameters on the same examination object.

In order to train the algorithm 36, a cost function 80 is minimized by changing the parameters 37 of the algorithm 36, which cost function depends on the difference between the measure 79 for the noise in the second image data set 76 and the measure 78 for the noise in the sum data set 77. The sum data set 77 is determined by applying the algorithm 36 to be trained to the first image data set 75 and adding the resulting data set formed to the second image data set 76. The change of the parameters 37 of the algorithm 36 can be performed, for example, by error feedback known per se.

Referring to fig. 6 and 7, the structure of an algorithm that can be trained by machine learning is set forth below in the example of a neural network or convolutional neural network to provide an algorithm 36 for reducing image noise. The structures are described in simple examples, respectively, which can be correspondingly extended for real applications.

Fig. 6 shows an embodiment of the artificial neural network 1. The english expression for the artificial neural network 1 is "artificial neural network", "artificial neural network", or "neural network".

The artificial neural network 1 includes nodes (nodes) 6 to 18 and edges (edges) 19 to 21, wherein each edge 19 to 21 is a directional connection from a first node 6 to 18 to a second node 6 to 18. Typically, the first node 6 to 18 and the second node 6 to 18 are different nodes 6 to 18, however, it is also conceivable that the first node 6 to 18 and the second node 6 to 18 are identical. For example, in FIG. 6, edge 19 is the directed connection from node 6 to node 9, and edge 21 is the directed connection from node 16 to node 18. Edges 19 to 21 from the first nodes 6 to 18 to the second nodes 6 to 18 are referred to as input edges ("entering edges") for the second nodes 6 to 18, and as output edges ("outputting edges") for the first nodes 6 to 18.

In this embodiment, the nodes 6 to 18 of the artificial neural network 1 may be arranged in layers (layers) 2 to 5, wherein the layers 2 to 5 may have an inherent order, which is introduced by the edges 19 to 21 between the nodes 6. In particular, the edges 19 to 21 can only be arranged between adjacent layers of the node. In the embodiment shown, there is an input layer 2 having only nodes 6, 7, 8, each without an input edge. The output layer 5 comprises only nodes 17, 18, each without an output edge, wherein furthermore the hidden layers 3 and 4 are located between the input layer 2 and the output layer 5. In the general case, the number of hidden layers 3, 4 can be chosen arbitrarily. The number of nodes 6, 7, 8 in the input layer 2 generally corresponds to the number of input values into the neural network 1, and the number of nodes 17, 18 in the output layer 5 generally corresponds to the number of output values of the neural network 1.

In particular, the nodes 6 to 18 of the neural network 1 may be associated with (real) numbers. Here, x⁽ⁿ⁾ _iRepresents the value of the ith nodes 6 to 18 in the nth layers 2 to 5. The values of the nodes 6, 7, 8 in the input layer 2 are equal to the input values of the neural network 1, while the values of the nodes 17, 18 in the output layer 113 are equal to the output values of the neural network 1. Furthermore, each edge 19, 20, 21 may be associated with a weight in the form of a real number. In particular, the weight is the interval [ -1, 1 [ ]]Middle or interval [0, 1 ]]Real number in (2). Here, w^(m,n) _i,jRepresents the weight of the edge between the ith node 6 to 18 in the mth layer 2 to 5 and the jth node 6 to 18 in the nth layer 2 to 5. In addition, a weight forFor short of

To calculate the output values of the neural network 1, the input values are propagated through the neural network 1. Specifically, the values of the nodes 6 to 18 of the (n +1) th layers 2 to 5 may be calculated by the following equations based on the values of the nodes 6 to 18 of the nth layers 2 to 5:

here, f is a transfer function, which may also be referred to as an activation function. Known transfer functions are step functions, sigmoid functions (e.g. logistic function, generalized logistic function, hyperbolic tangent, arctangent, error function, smoothing step function) or rectification functions (recitifiers). The transfer function is basically used for normalization purposes.

In particular, the values are propagated layer by layer through the neural network 1, wherein the input data through the neural network 1 gives the values of the input layer 2. The value of the first hidden layer 3 may be calculated based on the value of the input layer 2 of the neural network 1, the value of the second hidden layer 4 may be calculated based on the value in the first hidden layer 3, and so on.

In order to be able to determine the values for the edges 19 to 21The neural network 1 must be trained using training data. In particular, the training data comprises training input data and training output data, which are denoted t below_i. For the training step, the neural network 1 is applied to the training input data in order to determine the calculated output data. In particular, the training output data and the calculated output data comprise several values, wherein the number is determined as the number of nodes 17, 18 in the output layer 5.

In particular, a comparison between the calculated output data and the training output data is used in order to recursively match the weights (back propagation algorithm ") inside the neural network 1. In particular, the weight may be changed corresponding to the following equation,

where γ is the learning rate, and if the (n +1) th layer is not the output layer 5, it is based onCan convert numbers into numbersIs recursively calculated as

And if the (n +1) th layer is the output layer 5, the number may be changedIs recursively calculated as

Wherein f' is the first derivative of the activation function, andis the comparison training value for the jth node 17, 18 in the output layer 5.

An example for a Convolutional Neural Network (CNN) is also given below in view of fig. 7. Here, it should be noted that the expression "Layer" is used here slightly differently from a Layer for a conventional neural network. For conventional neural networks, the expression "layer" refers only to a set of nodes in a layer, and thus only to a specific generation of nodes. For convolutional neural networks, the expression "layer" is typically used as the object of actively changing data, in other words, as a set of nodes of the same generation and either a set of input edges or a set of output edges.

Fig. 7 shows an embodiment of the convolutional neural network 22. In the illustrated embodiment, Convolutional neural network 22 includes an input Layer 23, a Convolutional Layer 24(Convolutional Layer), a pooling Layer 25, a fully-connected Layer 26, and an output Layer 27. In alternative designs, convolutional neural network 22 may contain multiple convolutional layers 24, multiple pooling layers 25, and multiple fully-connected layers 26, among other types of layers. The order of the layers can be chosen arbitrarily, wherein the fully connected layer 26 usually forms the last layer before the output layer 27.

In particular, within the convolutional neural network 22, the nodes 28 to 32 in one of the layers 23 to 27 may be arranged as a d-dimensional matrix or as a d-dimensional image.In particular, in the case of two dimensions, the value of the nodes 28 to 32 with the subscripts i, j in the nth layers 23 to 27 may be represented as x⁽ⁿ⁾[i,j]. It should be noted that the arrangement of the nodes 28 to 31 in the layers 23 to 27 has no influence on the calculations inside the convolutional neural network 22 itself, since this influence is given only by the structure and the weights of the edges.

Convolutional layer 24 is characterized, inter alia, in that the structure and weights of the input edges form a convolution operation based on a certain number of kernels. In particular, the structure and weights of the input edges may be selected such that the values of nodes 29 in layer 24 will be convolvedDetermined as a value x based on a node 28 in the previous layer 23^(n-1)Is convolved withWherein the convolution may be defined as in the case of two dimensions

Here, the kth core K_kIs a d-dimensional matrix, in this embodiment a two-dimensional matrix, which is typically small compared to the number of nodes 28-32, for example a 3x3 matrix or a 5 x 5 matrix. In particular, this means that the weights of the input edges are not independent, but are chosen such that the weights of the input edges generate the above-mentioned convolution equation. In the example for the cores forming the 3x3 matrix, there are only nine independent weights (where each entry in the core matrix corresponds to one independent weight) regardless of the number of nodes 28 to 32 in the corresponding layers 23 to 27. In particular, for convolutional layer 24, the number of nodes 29 in convolutional layer 24 is equal to the number of nodes 28 in previous layer 23 multiplied by the number of convolution kernels.

If the nodes 28 in the upper layer 23 are arranged as a d-dimensional matrix, the use of multiple cores may be understood as adding an additional dimension, also referred to as a depth dimension, such that the nodes 29 in the convolutional layer 24 are arranged as a (d +1) -dimensional matrix. If the nodes 28 in the previous layer 23 have been arranged as a (d +1) -dimensional matrix with a depth dimension, the use of multiple convolution kernels can be understood as an extension along the depth dimension, such that the nodes 29 in the convolution layer 221 are also arranged as a (d +1) -dimensional matrix, wherein the size of the (d +1) -dimensional matrix in the depth dimension is larger than the coefficients formed by the number of kernels in the previous layer 23.

An advantage of using convolutional layers 24 is that by creating a local connection pattern between nodes in adjacent layers, the spatial local correlation of the input data can be exploited, in particular since each node has connections only for a small area of nodes in the previous layer.

In the illustrated embodiment, the input layer 23 includes 36 nodes 28 arranged as a two-dimensional 6 x 6 matrix. Convolutional layer 24 comprises 72 nodes 29 arranged as two-dimensional 6 x 6 matrices, where each of the two matrices is the result of the convolution of the values of input layer 23 with a convolution kernel. In the same way, the nodes 29 in convolutional layer 24 may be understood as being arranged in a three-dimensional 6 x 2 matrix, where the last-mentioned dimension is the depth dimension.

The Pooling layer 25 is characterized in that the structure and weights of the input edges and their activation functions of the nodes 30 define a Pooling operation based on a non-linear Pooling function (Pooling-Funktion) f. For example, in the two-dimensional case, it may be based on the value x of the node 29 in the previous layer 24⁽ⁿ⁺¹⁾To convert the value x of a node 30 in the pooling layer 25⁽ⁿ⁾Is calculated as

x⁽ⁿ⁾[i,j]＝f(x^(n-1)[id₁,jd₂],…,x^(n-1)[id₁+d₁-1,jd₂+d₂-1])。

In other words, by replacing the number d of adjacent nodes 29 in the previous layer 24 by a single node 30, due to the use of the pooling layer 25_1*d₂The number of nodes 29, 30 can be reduced, the single node being calculated as a function of the value of said number of neighbouring nodes 29. In particular, the pooling function f may be a maximum function, a mean formation or an L2 norm. In particular for the pooling layer 25, the weight of the input edge may be determined and not changed by training.

The advantage of using the pooling layer 25 is that the number of nodes 29, 30 and the number of parameters is reduced. This results in a reduction of the amount of computation required inside the convolutional neural network 22 and thus in an inhibition of the overfitting.

In the illustrated embodiment, the pooling layer 25 is a maximum pooling layer in which four neighboring nodes are replaced by one single node, the value of which is formed by the maximum of the values of the four neighboring nodes. Applying maximum pooling to each d-dimensional matrix of a previous layer; in this embodiment, maximum pooling is applied to each of the two-dimensional matrices, such that the number of nodes is reduced from 72 to 18.

The fully-connected layer 26 is characterized by the presence of a plurality of edges, in particular all edges, between the node 30 in the previous layer 25 and the node 31 in the fully-connected layer 26, wherein the weight of each of the edges can be matched individually. In this embodiment, nodes 30 in layer 25 preceding fully connected layer 26 are shown as both a two-dimensional matrix and unconnected nodes (shown as a row of nodes, where the number of nodes has been reduced for better visibility). In this embodiment, the number of nodes 31 in the fully connected layer 26 is equal to the number of nodes 30 in the previous layer 25. In alternative embodiments, the number of nodes 30, 31 may be different.

Further, in this embodiment, the value of the node 32 in the output layer 27 is determined by applying the Softmax function to the value of the node 31 in the previous layer 26. By applying the Softmax function, the sum of the values of all nodes 32 in the output layer 27 is 1, and all the values of all the nodes 32 in the output layer are real numbers between 0 and 1. If the input data is classified using the convolutional neural network 22, the values of the output layer 27 may be interpreted specifically as a probability for the input data falling into one of the different classes.

The convolutional neural network 22 may also have a ReLU layer, where ReLU stands for the acronym for "linear rectification functions". In particular, the number of nodes and the structure of nodes inside the ReLU layer are equal to the number of nodes and the structure of nodes in the previous layer. The value of each node in the ReLU layer may be calculated, inter alia, by applying a rectification function (reciifier function) to the value of the corresponding node in the previous layer. Examples for a rectification function are f (x) max (0, x), hyperbolic tangent or an S-type function.

The convolutional neural network 22 may be trained based on, inter alia, a back propagation algorithm. To avoid overfitting, regularization methods may be used, such as loss of individual nodes 28 to 32, random pooling, use of artificial data, weight decay based on an L1 norm or an L2 norm or maximum norm limit.

Although the invention has been illustrated and described in more detail in the detail by means of preferred embodiments, the invention is not limited to the disclosed examples and other variants can be derived therefrom by the person skilled in the art without departing from the scope of protection of the invention.