阅读说明：本技术 吸收系数图像估计方法、吸收系数图像估计程序以及安装有该吸收系数图像估计程序的正电子ct装置 (Absorption coefficient image estimation method, absorption coefficient image estimation program, and positron CT device having the absorption coefficient image estimation program installed therein ) 是由 小林哲哉 于 2017-05-29 设计创作，主要内容包括：在本发明的吸收系数图像估计方法中,基于区域(Ω)内的不定量的图像(μ’)的值与已知的吸收系数值(真实的吸收系数图像的值)之差能够以偏移图像(μ<Sub>off</Sub>)乘以系数α倍的α×μ<Sub>off</Sub>近似的数学关系,在步骤S8(μ＝μ’+α×μ<Sub>off</Sub>)中校正吸收系数值。因而,具有在步骤S8(μ＝μ’+α×μ<Sub>off</Sub>)中校正后的吸收系数值(μ)的吸收系数图像的系统误差变小。其结果,能够制作定量的吸收系数图像,因此能够进行放射性图像的准确的吸收校正。(In the absorption coefficient image estimation method of the present invention, the offset image (μ ') can be obtained based on the difference between the value of the indefinite amount of image (μ') within the region (Ω) and the known absorption coefficient value (value of the true absorption coefficient image) off ) Multiplying by a factor alpha times alpha x mu off Approximate mathematical relationship, in step S8(μ ═ μ' + α × μ ═ off ) Correcting the absorption coefficient value. Thus, the method includes the step S8(μ ═ μ' + α × μ ═ α × off ) The systematic error of the absorption coefficient image of the corrected absorption coefficient value (μ) becomes small. As a result, a quantitative absorption coefficient image can be created, and therefore, accurate absorption correction of the radioactive image can be performed.)

1. An absorption coefficient image estimation method for estimating an absorption coefficient image from measurement data of positron CT including information of a time difference of flight of annihilation radiation, the method comprising:

a reconstruction calculation step of calculating an image μ' by adding a non-uniform offset value to a quantitative absorption coefficient image, based on optimization of an evaluation function relating to the measurement data;

a mask calculation step of calculating object mask projection data, which is object mask data in a projection data space, based on the measurement data;

an offset estimation step of estimating a deviation of the measured value_offWhen the offset image is not uniform, the offset image mu is set_offEstimating the offset image mu by a reconstruction algorithm in which the forward projection data of (2) is configured to approximate the subject mask projection data_off；

A reference region extraction step of extracting at least one or more of the regions Ω, using an image that can identify a subject region calculated based on the measurement data, when Ω is set to a region that can be approximated by a known absorption coefficient value;

a coefficient calculation step of calculating a coefficient α that reduces an error between a value of the image μ' in the region Ω and a known absorption coefficient value, when α is set as the coefficient; and

an absorption coefficient value correction step of adding the value of the image [ mu ] to the offset image [ mu ]_offA x mu multiplied by said factor a_offThe resulting value is corrected as an absorption coefficient value.

2. The absorption coefficient image estimation method according to claim 1,

the reconstruction calculation step is performed by (a) a calculation algorithm including the image μ 'in an unknown number, or (b) a combination of a calculation algorithm including absorption coefficient projection data in an unknown number and an algorithm for reconstructing an image obtained by the absorption coefficient projection data as the image μ'.

3. The absorption coefficient image estimation method according to claim 1 or 2,

(A) the mask calculation process includes the following processes:

calculating a binarized image of the image μ' as a subject mask image;

calculating projection data of the subject mask image; and

calculating binarization data of projection data of the subject mask image as the subject mask projection data,

alternatively, (B) the mask calculation step includes the steps of:

calculating projection data of the image μ'; and

binarized data of the projection data of the image μ' is calculated as the object mask projection data.

4. The absorption coefficient image estimation method according to claim 1 or 2,

the mask calculation process includes the following processes: data obtained by binarizing data obtained by converting the measurement data into a projection data format is calculated as the object mask projection data.

5. The absorption coefficient image estimation method according to claim 1 or 2,

(C) the mask calculation process includes the following processes:

calculating a radiological image based on an optimization of an evaluation function related to the measurement data;

calculating projection data of the radiological image; and

calculating data obtained by binarizing the projection data as the object mask projection data,

alternatively, (D) the mask calculation step includes the steps of:

calculating a radiological image based on an optimization of an evaluation function related to the measurement data;

calculating a binary image of the radioactive image;

calculating projection data of the binary image; and

data obtained by binarizing the projection data of the binarized image is calculated as the object mask projection data.

6. The absorption coefficient image estimation method according to any one of claims 1 to 5,

the reconstruction process performed in the offset estimation step is performed by any one of an analytical reconstruction, a statistical reconstruction, and an algebraic reconstruction.

7. The absorption coefficient image estimation method according to any one of claims 1 to 6,

the at least one region Ω extracted in the reference region extraction step is a region of a tissue in which an absorption coefficient can be regarded as known.

8. The absorption coefficient image estimation method according to any one of claims 1 to 7,

setting K as the number of regions that can be approximated by a known absorption coefficient value, and setting Ω_nSetting the nth region omega to be muⁿ _known(n is 1, …, K) is the region Ω_nKnown value of the absorption coefficient, S (X; omega)_n) Set to said region Ω_nThe statistic of the image X or the representative value of the values calculated from the statistic, and T (X)₁，x₂，…，x_K) Set to arbitrary K values x₁，x₂，…，x_KOr a representative value of the values calculated from the statistical amount, will be alpha_nSet to said region Ω_nIn the coefficient calculation step, the coefficient α is α ═ T (α ═ T) (α₁，α₂，…，α_K)，α_n＝(μⁿ _known-S(μ'；Ω_n))/S(μ_off；Ω_n) (n is 1, …, K), wherein K is more than or equal to 1.

9. The absorption coefficient image estimation method according to any one of claims 1 to 7,

setting K as the number of regions that can be approximated by a known absorption coefficient value, and setting Ω_nSetting the nth region omega to be muⁿ _known(n is 1, …, K) is set to be in the region Ω_nImage with known absorption coefficient set therein, image D_Ωn(X, Y) is set to be equal to the region omega_nError evaluation function of inter-related image X and image Y, w_n(n is 1, …, K) is a coefficient of 0 to 1, and the coefficient α in the coefficient calculation step is a function f (α) of Σ_{n＝1，…，K}[w_n×D_Ωn(μⁿ _known，μ'+α×μ_off)]Minimized alpha, wherein K.gtoreq.1.

10. An absorption coefficient image estimation program for causing a computer to execute an absorption coefficient image estimation method according to any one of claims 1 to 9.

11. A positron CT device having the absorption coefficient image estimation program according to claim 10 installed thereon,

the positron CT apparatus includes an arithmetic unit for executing the absorption coefficient image estimation program.

Technical Field

The present invention relates to an absorption coefficient image estimation method and an absorption coefficient image estimation program for estimating an absorption coefficient image from measurement data of a positron CT apparatus (positron emission tomography apparatus), and a positron CT apparatus having the absorption coefficient image estimation program installed therein.

Background

A Positron Emission Tomography (PET) device, which is a Positron CT device, is configured to: only when two gamma rays generated by annihilation of positrons (positrons) are simultaneously detected by a plurality of detectors (that is, only when simultaneous counting is performed), the two gamma rays are measured as effective signals, and a tomographic image of the object is reconstructed based on the measurement data. Specifically, a radiopharmaceutical containing a positron-emitting nuclide is administered to a subject, and an annihilation gamma ray pair of 511keV emitted from the subject to which the radiopharmaceutical is administered is detected by a detector including a plurality of detector element (e.g., scintillator) groups. When gamma rays are detected by two detectors within a fixed time, the gamma rays are detected "simultaneously", the simultaneously detected gamma rays are counted as an annihilation gamma ray pair, and a Line of response (LOR) connecting the two detectors that detected the annihilation occurrence position is determined. The coincidence count information thus detected is stored and subjected to reconstruction processing, thereby obtaining a positron-emitting nuclide image (i.e., a tomographic image).

In positron ct (pet), various data correction processes are required to quantitatively measure the radioactive concentration in the subject. Representative correction processes are sensitivity correction, scatter correction, random correction, attenuation correction, dead time correction, and absorption correction. The present invention relates to an absorption correction for preventing quantitative reduction of an image caused by absorption of gamma rays emitted from a radiopharmaceutical (radioisotope). In order to perform absorption correction, it is necessary to estimate an absorption coefficient image obtained by imaging the absorption coefficient distribution in the subject.

In the absorption correction, the transmittance of the gamma ray is obtained from the estimated absorption coefficient image, and the PET measurement data is converted into data excluding the influence of the absorption of the gamma ray by dividing the transmittance. Alternatively, the estimated absorption coefficient image is incorporated into an image reconstruction calculation formula to obtain a reconstructed image from which the influence of the absorption of the γ -ray is eliminated.

In order to estimate the absorption coefficient image, Transmission data obtained by irradiating an external ray source of an positron emitting nuclear species is required. Alternatively, the absorption coefficient image can be estimated using CT data obtained from an X-ray CT (computed tomography) apparatus instead of the transmission data.

In recent years, there is a reconstruction algorithm that does not require such transmission data (see, for example, non-patent documents 1 and 2). In non-patent documents 1 and 2, the distribution shape Of the absorption coefficient sinogram can be estimated from measurement data Of PET (hereinafter, referred to as "TOF-PET") for measuring Time difference Of detection (also referred to as "Time Of Flight") information Of annihilation radiation (TOF). Moreover, the radiological image and the absorption coefficient sinogram can be estimated simultaneously. Since the radiological image and the data relating to the absorption coefficient (for example, an absorption coefficient sinogram) are estimated at the same time, the reconstruction algorithms in non-patent documents 1 and 2 are also referred to as "simultaneous reconstruction algorithms". In particular, a simultaneous reconstruction algorithm that simultaneously estimates a radiological image and an absorption coefficient sinogram is also called an MLACF method.

The principle of the MLACF method is qualitatively explained with reference to the conceptual diagram of fig. 9. The radioactive concentration in the target region of the subject is distributed as shown in fig. 9. When the radioactivity distribution is developed into a two-dimensional distribution composed of TOF information t and a radial direction s, the projection direction θ becomes 0 °, as in the upper diagram of fig. 9, and the projection direction θ becomes 90 °, as in the right diagram of fig. 9. In a range where the projection direction θ is made 0 ° to 180 °, a respective two-dimensional distribution of each projection angle θ is obtained as measurement data.

If there is no absorption of gamma rays, the two-dimensional distribution at each projection angle θ can be restored to the original radioactivity distribution. However, in practice, the gamma ray is absorbed and thereby returns to a different radioactivity distribution from the original one. In addition, the degree of absorption of gamma rays varies depending on the projection direction. As shown in fig. 9, when a is taken as the degree of absorption when the projection direction θ is 0 ° and a 'is taken as the degree of absorption when the projection direction θ is 90 °, a ≠ a' is normal. Therefore, by using the measurement data of the TOF information, the error between the measurement data and the estimation data obtained by multiplying the unknown absorption coefficient value by the projection data is minimized, and thereby the absorption coefficient sinogram in which the absorption coefficient value is converted into the sinogram form can be estimated while estimating the radiological image.

However, only the distribution shape (i.e., relative value) that can be estimated cannot be estimated as an absolute value. If the absolute value of the absorption coefficient sinogram is not judged, absorption correction cannot be accurately performed. Thus, quantitative radioactive images cannot be acquired. This is a clinical problem and is a serious obstacle to practical use.

For practical application of the PET imaging technique based on the simultaneous reconstruction algorithm, a technique such as that described below is indispensable. That is, a technique of estimating an absorption coefficient image whose absolute value is correct from an absorption coefficient sinogram whose distribution shape is correct but whose absolute value is wrong is indispensable.

Therefore, as a conventional technique of non-patent document 2, there is a method of directly quantifying a radiological image without directly quantifying an absorption coefficient sinogram. The processing steps are as follows.

(1) A radiological image without absorption correction is created, and a subject mask image is created from the radiological image.

(2) A virtual absorption coefficient image (hereinafter, simply referred to as "virtual absorption coefficient image") is created by substituting a known absorption coefficient (for example, an absorption coefficient of water or an absorption coefficient of bone) into each pixel value of the subject mask image.

(3) Using the virtual absorption coefficient image, a radiological image is created by a conventional reconstruction algorithm, and the total pixel value is calculated for each slice in the body axis direction. As shown in fig. 10, when z is a body axis direction, an xy plane is a plane (axial plane) orthogonal to the body axis direction z, P (x, y) is a pixel value, and s (z) is a total pixel value for each slice in the body axis direction z, s (z) ∑ Σ_yΣ_xP (x, y). When the horizontal axis is the body axis direction z and the vertical axis is the total pixel value s (z), a distribution diagram like the right diagram of fig. 10 is created.

(4) An infinite number of radioactive images and an infinite number of absorption coefficient sinograms are estimated by a simultaneous reconstruction algorithm.

(5) As for the variable quantity of radioactive images obtained in the process (4), the total pixel value is also calculated for each slice in the body axis direction, as in the process (3). Here, S' (z) is a total pixel value for each slice in the body axis direction z.

(6) The variable quantity of the radioactive image obtained in the process (4) is scaled and quantified so that the total pixel value S' (z) obtained in the process (5) coincides with the total pixel value S (z) obtained in the process (3) for each slice in the body axis direction. Specifically, the radioactive image is scaled by multiplying each pixel value of the indeterminate radioactive image obtained in the step (4) by S (z)/S' (z) for each slice in the body axis direction.

Disclosure of Invention

Problems to be solved by the invention

However, the prior art of the above non-patent document 2 has the following problems: in principle, it is not guaranteed that the finally determined radiological image is quantitative.

The present invention has been made in view of the above circumstances, and an object thereof is to provide an absorption coefficient image estimation method and an absorption coefficient image estimation program capable of creating a quantitative absorption coefficient image, and a positron CT apparatus incorporating the absorption coefficient image estimation program.

For solving the problemsScheme(s)

The inventors have made intensive studies to solve the above problems and as a result, have come to find out the following.

That is, the above-described prior art assumes that the total pixel value of each slice in the body axis direction found in the process (3) is true (i.e., correct).

However, it cannot be guaranteed that the total pixel value of each slice in the body axis direction obtained in the process (3) is correct. Since the quantification is performed based on a result that does not guarantee accuracy, the quantification of the radiological image obtained in step (6) cannot be guaranteed. Therefore, the conventional technique has a problem that a quantitative radioactive image cannot be generated. That is, the following finding is made: the source of the problems of the prior art is an empirical method, not a mathematical theory based on the background of the problem of quantification of the absorption coefficient.

The present invention based on this finding adopts the following configuration.

That is, an absorption coefficient image estimation method according to the present invention is a method for estimating an absorption coefficient image from measurement data Of positron CT including Time Of Flight (Time Of Flight) information Of annihilation radiation, including the steps Of: a reconstruction calculation step of calculating an image μ' by adding a non-uniform offset value to a quantitative absorption coefficient image, based on optimization of an evaluation function relating to the measurement data; a mask calculation step of calculating object mask projection data, which is object mask data in a projection data space, based on the measurement data; an offset estimation step of estimating a deviation of the measured value_offWhen the offset image is not uniform, the offset image mu is set_offEstimating the offset image mu by a reconstruction algorithm in which the forward projection data of (2) is configured to approximate the subject mask projection data_off(ii) a A reference region extraction step of extracting at least one or more of the regions Ω, using an image that can identify a subject region calculated based on the measurement data, when Ω is set to a region that can be approximated by a known absorption coefficient value; a coefficient calculation step of, when a is set as a coefficient,calculating said coefficient a which reduces the error between the values of said image μ' within said region Ω and the known values of the absorption coefficient; and an absorption coefficient value correction step of adding the value of the image [ mu ] to the offset image [ mu ]_offA x mu multiplied by said factor a_offThe resulting value is corrected as an absorption coefficient value.

According to the absorption coefficient image estimation method Of the present invention, in the reconstruction calculation step, an image obtained by adding an uneven offset value to a quantitative absorption coefficient image is calculated based on optimization Of an evaluation function relating to positron CT measurement data (TOF-PET measurement data) including Time Of Flight (Time Of Flight) information Of annihilation radiation. Meanwhile, when λ 'is an unquantized radioactive image, the radioactive image λ' is calculated in the reconstruction calculation step. The reconstruction algorithm in the reconstruction calculation step here is the above-described simultaneous reconstruction algorithm. Here, when an image obtained by adding a non-uniform offset value to a quantitative absorption coefficient image is denoted by μ ', the image μ ' is also an absorption coefficient image, but is distinguished from the quantitative absorption coefficient image finally obtained, and is simply denoted by "image μ '".

On the other hand, in the mask calculation step, object mask data (hereinafter referred to as "object mask projection data") in the projection data space is calculated based on the measurement data. In the process of mixing_offIn the offset estimation step, the offset image μ is used to obtain a non-uniform offset image_offEstimating the offset image mu by a reconstruction algorithm configured to approximate the subject mask projection data_off。

On the other hand, when Ω is set to a region that can be approximated by a known absorption coefficient value, at least one or more regions Ω are extracted in the reference region extraction step using an image that can identify the subject region calculated based on the measurement data.

Here, the "image that can identify the object region calculated based on the measurement data" is, for example, the above-described image μ ', the above-described radiological image λ', an image that is non-quantitative and estimated by a reconstruction algorithm different from the reconstruction algorithm (simultaneous reconstruction algorithm) in the above-described reconstruction calculation step, or an object mask image estimated from the above-described object mask projection data. Of course, the present invention is not limited to these exemplary images, and may be any image that can identify the subject region calculated based on the measurement data. The phrase "at least one or more regions Ω are extracted using an image that can identify a region of a subject calculated based on measurement data" includes not only a case where the region Ω is extracted using a single piece of image information but also a case where the region Ω is extracted using a combination (for example, logical sum or logical product) of a plurality of pieces of image information.

Using the image μ' and the offset image μ obtained in the above steps_offAnd an area Ω for performing the following coefficient calculation step and absorption coefficient value correction step. When μ is set to a value of an unknown true absorption coefficient image (absorption coefficient value) and α is set to a coefficient, a coefficient α is calculated in the coefficient calculation step so that an error between a value of the image μ' in the region Ω and a known absorption coefficient value is reduced. Then, in the absorption coefficient value correction step, the offset image μ is added to the value of the image μ_offMultiplying by a factor alpha times alpha x mu_offThe resulting value is corrected as an absorption coefficient value. In this way, the absorption coefficient value is corrected in the absorption coefficient correction step based on a mathematical relationship that allows the difference between the value of the indefinite amount of image μ' in the region Ω and the known absorption coefficient value (the value of the true absorption coefficient image) to shift the image μ_offMultiplying by a factor alpha times alpha x mu_offApproximation is performed (that is, μ ≈ μ' + α × μ_off). Therefore, the systematic error of the absorption coefficient image having the absorption coefficient value corrected in the absorption coefficient value correction step becomes small. As a result, a quantitative absorption coefficient image can be created, and therefore, accurate absorption correction of the radioactive image can be performed.

The reconstruction calculation step may be performed by (a) a calculation algorithm including an image μ' in an unknown number. Alternatively, the reconstruction calculation step may be performed by a combination of (b) a calculation algorithm including absorption coefficient projection data in an unknown number and an algorithm for reconstructing an image obtained by the absorption coefficient projection data as the image μ'.

The former algorithm (a) is an MLAA method in which an unquantized radioactivity image λ 'and an image μ' (an unquantized absorption coefficient image) are reconstructed at the same time. The algorithm (b) of the latter is a combination of the MLACF method described in non-patent document 1, which estimates both the non-quantitative radioactive image λ 'and the non-quantitative absorption coefficient projection data (for example, an absorption coefficient sinogram), and an algorithm for reconstructing an image obtained by the absorption coefficient projection data as an image μ'. The algorithm for reconstructing the image obtained by reconstructing the absorption coefficient projection data as the image μ' in the latter (b) is not particularly limited as long as it is a reconstruction algorithm.

An example of the mask calculation step includes the following steps (mode (a)): calculating a binary image of the image mu' as a subject mask image; calculating projection data of a subject mask image; and calculating binarization data of projection data of the subject mask image as subject mask projection data. The mask calculation step may be an embodiment (B) including the following steps: calculating projection data of the image mu'; and calculating binarized data of the projection data of the image μ' as object mask projection data. In the above-described method (a), the projection data is calculated after the image μ' is binarized, and the projection data is binarized. In the above-described mode (B), the projection data of the image μ' is calculated first, and then binarization is performed. The image μ' is an absorption coefficient image of a variable amount, but even if images other than the absorption coefficient image and projection data are binarized, the subject mask projection data can be calculated.

Another example of the mask calculation process includes the following processes: data obtained by binarizing data obtained by converting the TOF-PET measurement data into a projection data format is calculated as object mask projection data. In this example, data obtained by binarizing data obtained by converting measurement data directly using TOF-PET into a projection data format can be calculated as object mask projection data.

Another example of the mask calculation step is an embodiment (C) including the following steps: calculating a radiological image based on an optimization of an evaluation function related to the measurement data of TOF-PET (described above); calculating projection data of the radioactive image; and calculating data obtained by binarizing the projection data (of the radiological image) as object mask projection data. The mask calculation step may be a method (D) including the following steps: calculating a radiological image based on an optimization of an evaluation function related to the measurement data of TOF-PET (described above); calculating a binary image of the radioactive image; calculating projection data of the binary image; data obtained by binarizing the projection data of the binarized image is calculated as object mask projection data. In the method (C), projection data of a radiological image is calculated first, and then binarized. In the method (D), projection data is calculated after the radioactive image is binarized, and the projection data is binarized. In both the above-described method (C) and the above-described method (D), a reconstruction algorithm for calculating a radiological image is not particularly limited in this example. When the simultaneous reconstruction algorithm (the MLACF method or the MLAA method) is used, the subject mask projection data can be calculated using the radiological image λ' estimated by the simultaneous reconstruction algorithm. The subject mask projection data may be calculated using a radiological image estimated by a reconstruction algorithm (for example, ML-EM method) different from the above-described simultaneous reconstruction algorithms (MLACF method, MLAA method).

The reconstruction process performed in the offset estimation step may be performed by any one of the calculation methods of analysis reconstruction, statistical reconstruction, and algebraic reconstruction. As the analytical reconstruction, there is, for example, an FBP (Filtered Back Projection) method. As the statistical reconstruction, for example, there is the ML-EM (Maximum Likelihood-Expectation Maximization) method described above. As the Algebraic Reconstruction, there is an ART (Algebraic Reconstruction) method, for example.

The at least one region Ω extracted in the reference region extraction step is a region of a tissue in which the absorption coefficient can be regarded as known. Here, "a region in which the absorption coefficient can be regarded as a known tissue" is, for example, a region that can be approximated by water, a region that can be approximated by air, a region that can be approximated by brain tissue, a region that can be approximated by bone, a region that can be approximated by lung tissue, a region that can be approximated by soft tissue, or the like. Of course, the present invention is not limited to these exemplified structures, and any structure may be used as long as the approximate value of the absorption coefficient is known. In the case of brain tissue, since it is considered to be a region that can be approximated by water, 0.0096/mm, which is an absorption coefficient value of water, can be used.

The coefficient α in the coefficient calculation step includes a method of calculating based on the representative value (the former method) as described below and a method of calculating based on the error evaluation function (the latter method) as described below.

In the former method, K (. gtoreq.1) is set to the number of regions that can be approximated by a known absorption coefficient value, and Ω_nLet μ be the nth region Ωⁿ _known(n is 1, …, K) is a region Ω_nIs given by the known absorption coefficient value of S (X; omega)_n) Is set to region Ω_nThe statistic of the image X or the representative value of the values calculated from the statistic is represented by T (X)₁，x₂，…，x_K) Set to arbitrary K values x₁，x₂，…，x_KOr a representative value of the values calculated from the statistics, and alpha_nIs set to region Ω_nThe coefficient a within. Here, the representative value is, for example, an average value, a median value, a truncated mean value, a truncated median value, or a weighted average of two or more of these. Of course, the present invention is not limited to these exemplified values, and may be "a statistical amount or a value calculated from a statistical amount".

If image X is replaced by image μ ', S (μ'; Ω)_n) Is the region omega_nIf the image X is replaced by an offset image mu_off', then S (mu)_off；Ω_n) Is the region omega_nIntra offset image mu_off' A representative value. Region omega_nKnown value of the absorption coefficient μⁿ _knownAnd to region omega_nRepresentative value S (μ'; Ω) of the inner image μ_n) Plus make region omega_nIntra offset image mu_off' representative value S (. mu.)_off；Ω_n) Multiplication by the region omega_nInner coefficient alpha_nRear alpha_n×S(μ_off；Ω_n) The obtained values are equal. That is, μⁿ _known＝S(μ'；Ω_n)+α_n×S(μ_off；Ω_n) This is true. Thus, by α_n＝(μⁿ _known-S(μ'；Ω_n))/S(μ_off；Ω_n) To calculate the region omega respectively_nInner coefficient alpha_n. If K is valued x₁，x₂，…，x_KRespectively substituted by alpha₁，α₂，…，α_KThen T (α)₁，α₂，…，α_K) Is coefficient alpha₁，α₂，…，α_KIs a representative value of (a). In short, each region Ω is calculated by n being 1, …, and K₁，…，Ω_KInner coefficient alpha₁，…，α_KThereafter, by applying the coefficient α₁，…，α_KRepresentative value of (a)₁，α₂，…，α_K) The coefficient α can be calculated by using the coefficient α.

In the latter method, K (. gtoreq.1) is set to the number of regions that can be approximated by a known absorption coefficient value, and Ω_nLet μ be the nth region Ωⁿ _known(n is 1, …, K) is defined as being in the region Ω_nAn image with a known absorption coefficient set therein, D_Ωn(X, Y) is equal to the region omega_nError evaluation function of inter-related image X and image Y, w_n(n is 1, …, K) is a coefficient of 0 to 1. If the image X is replaced in the region omega_nImage mu with a known absorption coefficient set thereinⁿ _knownAnd replacing the image Y with the offset image mu_off' multiplication by a factor of alpha x mu_offValue obtained by adding the image mu(μ'+α×μ_off) Then D is_Ωn(μⁿ _known，μ'+α×μ_off) Set the sum-region omega_nImage mu of known absorption coefficient of inner correlationⁿ _knownAnd an image obtained by adding a non-uniform offset value to the quantitative absorption coefficient image (μ' + α × μ)_off) The error evaluation function of (1). By calculating a function f (α) having a coefficient α as a variable (∑ e)_{n＝1，…，K}[w_n×D_Ωn(μⁿ _known，μ'+α×μ_off)]) The coefficient α can be calculated by minimizing α by using each region Ω in the case where n is 1, …, and K as the function f (α)₁，…，Ω_KRespective coefficient w₁，…，w_KCarry out D_Ω1(μ¹ _known，μ'+α×μ_off)，…，D_ΩK(μ^K _known，μ'+α×μ_off) Is obtained by weighted addition of (a).

The absorption coefficient image estimation program according to the present invention is configured to cause a computer to execute the absorption coefficient image estimation method according to the present invention.

According to the absorption coefficient image estimation program of the present invention, the absorption coefficient value is corrected in the absorption coefficient value correction step based on the mathematical relationship that the difference between the value of the indefinite amount image μ' in the region Ω and the known absorption coefficient value (the value of the true absorption coefficient image) can be shifted by the offset image μ by causing the computer to execute the absorption coefficient image estimation method of the present invention_offMultiplying by a factor alpha times alpha x mu_offAn approximation is made. Therefore, the systematic error of the absorption coefficient image having the absorption coefficient value corrected in the absorption coefficient value correction step becomes small. As a result, a quantitative absorption coefficient image can be created, and therefore, accurate absorption correction of the radioactive image can be performed.

In addition, the positron CT apparatus according to the present invention includes an arithmetic unit for executing the absorption coefficient image estimation program in the positron CT apparatus in which the absorption coefficient image estimation program according to the present invention is installed.

According to the positron CT apparatus of the present invention, by including the arithmetic means for executing the absorption coefficient image estimation program of the present invention, the absorption coefficient value is corrected in the absorption coefficient value correction step based on the mathematical relationship that the difference between the value of the indefinite amount image μ' in the region Ω and the known absorption coefficient value (the value of the true absorption coefficient image) can be shifted by the offset image μ_offMultiplying by a factor alpha times alpha x mu_offAn approximation is made. Therefore, the systematic error of the absorption coefficient image having the absorption coefficient value corrected in the absorption coefficient value correction step becomes small. As a result, a quantitative absorption coefficient image can be created, and therefore, accurate absorption correction of the radioactive image can be performed.

ADVANTAGEOUS EFFECTS OF INVENTION

According to the absorption coefficient image estimation method, the absorption coefficient image estimation program, and the positron CT apparatus having the absorption coefficient image estimation program installed therein of the present invention, the absorption coefficient value is corrected in the absorption coefficient value correction step based on the mathematical relationship that the difference between the value of the indefinite amount image μ' in the region Ω and the known absorption coefficient value (the value of the true absorption coefficient image) can shift the image μ_offMultiplying by a factor alpha times alpha x mu_offTo make an approximation. Therefore, the systematic error of the absorption coefficient image having the absorption coefficient value corrected in the absorption coefficient value correction step becomes small. As a result, a quantitative absorption coefficient image can be created, and therefore, accurate absorption correction of the radioactive image can be performed.

Drawings

Fig. 1 is a schematic perspective view and a block diagram of a PET apparatus according to each embodiment.

Fig. 2 is a schematic perspective view of the gamma-ray detector.

Fig. 3 is a flowchart showing a processing procedure and a data flow of the absorption coefficient image estimation method according to embodiment 1.

Fig. 4 is a flowchart showing a processing procedure and a flow of data of the absorption coefficient image estimation method according to embodiment 2.

Fig. 5 is a flowchart showing a processing procedure of the absorption coefficient image estimation method according to embodiment 3 and a flow of data in a case where the object mask projection data is calculated using the radiological image estimated by the MLACF method.

Fig. 6 is a flowchart showing a processing procedure of the absorption coefficient image estimation method according to embodiment 3 and a flow of data in the case of calculating object mask projection data using a radiological image estimated by a reconstruction algorithm different from the MLACF method.

Fig. 7 is a flowchart showing a processing procedure and a flow of data of the absorption coefficient image estimation method according to embodiment 4.

Fig. 8 is a flowchart showing a processing procedure and a flow of data of the absorption coefficient image estimation method according to embodiment 5.

Fig. 9 is a conceptual diagram for explaining the principle of the MLACF method.

Fig. 10 is a schematic diagram of a total pixel value for each slice in the body axis direction and a curve in which the horizontal axis is the body axis direction and the vertical axis is the total pixel value.

Detailed Description

Hereinafter, embodiment 1 of the present invention will be described with reference to the drawings. Fig. 1 is a schematic perspective view and a block diagram of a PET apparatus according to each embodiment, and fig. 2 is a schematic perspective view of a gamma-ray detector. In fig. 1 and 2, the same structure is applied to each embodiment.

As shown in fig. 1, the PET apparatus 1 includes a detector ring 2 surrounding the periphery of a subject, and the detector ring 2 is stacked in the body axis direction of the subject. A plurality of gamma-ray detectors 3 are embedded in the detector ring 2. The PET apparatus 1 corresponds to a positron CT apparatus of the present invention. The gamma-ray detector 3 corresponds to the detector of the present invention.

In addition, the PET apparatus 1 includes a coincidence counting circuit 4 and an arithmetic circuit 5. In fig. 1, only two connection lines connecting the gamma-ray detector 3 to the coincidence counting circuit 4 are shown, but actually, the coincidence counting circuit 4 is connected with a number of connection lines corresponding to the total number of channels of the photomultiplier Tube (PMT)33 (see fig. 2) of the gamma-ray detector 3. The arithmetic circuit 5 executes processing of an absorption coefficient image estimation method shown in fig. 3 described later based on the absorption coefficient image estimation program 6. The arithmetic circuit 5 corresponds to an arithmetic unit of the present invention.

The scintillator block 31 (see fig. 2) of the gamma-ray detector 3 converts the gamma rays emitted from the subject (not shown) to which the radiopharmaceutical is administered into light, and the photomultiplier tube (PMT)33 (see fig. 2) of the gamma-ray detector 3 multiplies the converted light and converts it into an electrical signal. The electric signal is sent to the coincidence counting circuit 4 to generate detection signal data of a count value.

Specifically, when a radiopharmaceutical is administered to a subject (not shown), two gamma rays are generated due to positron annihilation of a positron-emitting RI. The coincidence counting circuit 4 checks the positions of the scintillator blocks 31 (see fig. 2) and the incidence timing of the gamma rays, and determines the input electric signals as appropriate data only when the gamma rays simultaneously enter two scintillator blocks 31 located on both sides of the subject. When a gamma ray is incident on only one of the scintillator blocks 31, the coincidence counting circuit 4 discards the electric signal. That is, the coincidence counting circuit 4 detects the gamma rays observed (i.e., coincidentally counted) at the two gamma-ray detectors 3 at the same time based on the electric signals described above.

Detection signal data (count value) composed of appropriate data determined to be simultaneously counted by the coincidence counting circuit 4 is supplied to the arithmetic circuit 5. The arithmetic circuit 5 performs steps S1 to S8 (see fig. 3) described later, and estimates an absorption coefficient image from detection signal data of a subject (not shown) obtained by the PET apparatus 1. The specific function of the arithmetic circuit 5 will be described later.

The absorption coefficient image estimation program 6 is stored in a storage medium (not shown) represented by a ROM (Read-only Memory) or the like, the absorption coefficient image estimation program 6 is Read out from the storage medium, the absorption coefficient image estimation program 6 is sent to the arithmetic circuit 5, and the arithmetic circuit 5 executes the absorption coefficient image estimation program 6, thereby performing the processing of the absorption coefficient image estimation method shown in the flowchart of fig. 3. The arithmetic circuit 5 is constituted by a GPU (Graphics processing unit), a Central Processing Unit (CPU), a Programmable device (e.g., a Field Programmable Gate Array (FPGA)) capable of changing a hardware circuit (e.g., a logic circuit) used therein in accordance with program data, and the like.

As shown in fig. 2, the gamma-ray detector 3 includes a scintillator block 31, a light guide 32 optically coupled to the scintillator block 31, and a photomultiplier tube (hereinafter, abbreviated as "PMT") 33 optically coupled to the light guide 32. Each scintillator element constituting the scintillator block 31 emits light in response to incidence of the gamma rays, thereby converting the gamma rays into light. The scintillator element detects gamma rays by this conversion. The light emitted in the scintillator element is sufficiently diffused in the scintillator block 31 and is input to the PMT 33 via the light guide 32. The PMT 33 multiplies the light converted by the scintillator block 31 and converts the multiplied light into an electric signal. The electric signal is sent to the coincidence counting circuit 4 (see fig. 1) as a pixel value.

In addition, as shown in fig. 2, the gamma ray detector 3 is a DOI detector including scintillator elements arranged three-dimensionally and including a plurality of layers in the depth direction. Fig. 2 illustrates a DOI detector having 4 layers, but the number of layers is not particularly limited as long as it is a multilayer.

Here, the DOI detector is configured by stacking scintillator elements in the Depth direction of the radiation, and obtains coordinate information in the Depth (Depth of Interaction) direction and the lateral direction (direction parallel to the incident surface) in which the Interaction occurs by the centroid calculation. By using the DOI detector, the spatial resolution in the depth direction can be further improved. Therefore, the number of layers of the DOI detector is the number of layers of scintillator elements stacked in the depth direction.

Next, a specific function of the arithmetic circuit 5 will be described with reference to fig. 3. Fig. 3 is a flowchart showing a processing procedure and data flow of the absorption coefficient image estimation method according to embodiment 1.

First, a subject is imaged by the PET apparatus 1 shown in fig. 1, and list mode data is acquired by the coincidence counting circuit 4 (see fig. 1). The list mode data records energy information of detected photons.

A general energy window (for example, 400keV to 600keV), that is, an energy window for reconstruction data, a measurement range in the TOF direction of TOF measurement data, and a segment width are set, respectively. Here, the segment (bin) means discretization (partitioning). In the case of an image, the pixels correspond to segments. TOF segment refers to time-division of TOF information, e.g., where the TOF segment is 100[ ps ], the detection time difference is temporally divided with an accuracy of every 100[ ps ].

According to this setting, measurement data of TOF-PET is created from the list mode data.

(step S1) MLACF

μ 'is an image obtained by adding a non-uniform offset value to a quantitative absorption coefficient image, and λ' is an non-quantitative radioactivity image. The image μ 'and the radiological image λ' are simultaneously calculated based on an optimization of an evaluation function related to the measurement data. As described in the section of "means for solving the problem", the image μ 'is also an absorption coefficient image, but is distinguished from a quantitative absorption coefficient image which is finally obtained, and is simply referred to as "image μ'".

The reconstruction algorithm in step S1 is the simultaneous reconstruction algorithm in non-patent document 1. In example 1, including examples 2 and 3 described later, the MLACF method described in non-patent document 1 is applied as a simultaneous reconstruction algorithm. As for a specific method of the MLACF method, reference is made to the above-mentioned non-patent document 1.

Set a' to the absorption coefficient sinogram. The radiological image λ 'and the absorption coefficient sinogram a' are estimated by the MLACF method. The absorption coefficient sinogram a' corresponds to the absorption coefficient projection data of the present invention.

(step S2) ML-TR or ML-EM

The absorption coefficient sinogram a 'is reconstructed using a reconstruction algorithm (e.g., ML-TR method, ML-EM method), and an image μ' of an indefinite amount is produced. In the case of the ML-EM method, the absorption coefficient sinogram a' is log-transformed in advance. As for a specific method of the ML-TR method, reference is made to reference 1 (reference 1: Erdo. Further, as for a specific method of the ML-EM method, reference is preferably made to reference 2 (reference 2: L.A. Shepp and Y.Vardi.maximum likelihood recovery for emission biology. IEEETrans. Med.imaging, Vol.1, pp.113-122, 1982). Steps S1 and S2 correspond to the reconstruction calculation step of the present invention.

(step S3) binarization processing

The image μ' is subjected to Binarization Processing (Binarization Processing) by threshold Processing. Then, a binarized image in which the subject region is "1" and the other regions are "0" is calculated as a subject mask image. M is to be_imgAn object mask image is set.

(step S4) projection + binarization processing

For the mask image m of the object_imgThe line integral data (projection data) of (a) is calculated (projected). Then, the mask image m of the subject is thresholded_imgThe projection data of (2) is subjected to Binarization Processing (Binarization Processing), thereby calculating binarized data in which a projection line passing through the subject is "1" and the other projection lines are "0", as subject mask projection data. M is to be_projThe subject mask projection data is set. Steps S3 and S4 correspond to the mask calculation step of the present invention.

(step S5) ML-EM

Mu to_offA non-uniform offset image is set. By configuring to shift the image mu_offIs projected on the mask of the object by the orthographic projection data m_projPerforming an approximate reconstruction algorithm to estimate the offset image mu_off. That is, the object mask projection data m is reconstructed by a reconstruction algorithm (for example, ML-EM method)_projAnd transformed into image data. Setting the image data as an offset image mu_off. Step S5 corresponds to the offset estimation process of the present invention.

(step S6) extraction

Ω is set as a region that can be approximated with a known absorption coefficient value. Using regions calculated on the basis of measurement data to enable identification of the subjectAt least one region Ω is extracted from the image (extraction). In example 1, including examples 2 to 4 described later, K (. gtoreq.1) is set to the number of regions that can be approximated by a known absorption coefficient value, and Ω_nWhen the nth region Ω is defined, each region Ω is extracted with n equal to 1, …, and K₁，…，Ω_K. For example, when the head of the subject is imaged, each region Ω is extracted as a region that can be approximated by air, a region that can be approximated by brain tissue, and a region that can be approximated by bone₁，…，Ω_K。

Examples of the image calculated based on the measurement data and capable of identifying the subject region include the image μ 'created in step S2, the radiological image λ' obtained in step S1, an image that is non-quantitative and estimated by a reconstruction algorithm (e.g., ML-EM method) different from the reconstruction algorithm (simultaneous reconstruction algorithm) in step S1, and the subject mask projection data m_pro_jEstimated object mask image m_img. Step S6 corresponds to the reference region extraction step of the present invention.

(step S7) a_n＝(μⁿ _known-S(μ'；Ω_n))/S(μ_off；Ω_n)，α＝T(α₁，α₂，…，α_K)

Mu toⁿ _known(n is 1, …, K) is a region Ω_nIs given by the known absorption coefficient value of S (X; omega)_n) Is set to region Ω_nThe statistic of the image X or the representative value of the values calculated from the statistic is represented by T (X)₁，x₂，…，x_K) Set to arbitrary K values x₁，x₂，…，x_KOr a representative value of the values calculated from the statistics, and alpha_nIs set to region Ω_nThe coefficient a within. Further, α is a coefficient. Here, the representative value is, for example, an average value, a median value, a trimmed mean value (trimmed mean), a trimmed median value, or a weighted average of two or more of these values. Here, the term "truncated mean" means that an extremely large/small value is removedAverage of the remaining data after the data. The "truncated central value" refers to a central value of data remaining after removing data whose value is extremely large/extremely small.

If image X is replaced by image μ ', S (μ'; Ω)_n) Is the region omega_nIf the image X is replaced by an offset image mu_off', then S (mu)_off；Ω_n) Is the region omega_nIntra offset image mu_off' A representative value. Region omega_nInner coefficient alpha_nThis is represented by the following formula (1).

α_n＝(μⁿ _known-S(μ'；Ω_n))/S(μ_off；Ω_n)…(1)

If K is valued x₁，x₂，…，x_KRespectively substituted by alpha₁，α₂，…，α_KThen T (α)₁，α₂，…，α_K) Is coefficient alpha₁，α₂，…，α_KIs a representative value of (a). Therefore, the coefficient α is expressed by the following expression (2). Step S7 corresponds to the coefficient calculation step of the present invention.

α＝T(α₁，α₂，…，α_k)…(2)

(step S8) μ ═ μ' + α × μ_off

μ is set to the value of the true absorption coefficient image (absorption coefficient value) which is unknown. The absorption coefficient μ is expressed by the following formula (3).

μ＝μ'+α×μ_off…(3)

The offset image μ is added to the value of the image μ' as in the above equation (3)_offMultiplying by a factor alpha times alpha x mu_offThe obtained value was corrected as an absorption coefficient value μ. Step S8 corresponds to the absorption coefficient value correction step of the present invention.

The absorption correction is performed using the absorption coefficient image having the absorption coefficient value μ found in step S8. As described in the section of "background art", the absorption correction is performed by obtaining the transmittance of gamma rays from the estimated absorption coefficient image, and converting the PET measurement data into data excluding the influence of the absorption of gamma rays by dividing the transmittance. Alternatively, absorption correction is performed by incorporating the estimated absorption coefficient image into an image reconstruction calculation formula to acquire a reconstructed image from which the influence of absorption by γ rays is removed.

According to the absorption coefficient image estimation method Of the present embodiment 1, in steps S1 and S2, an image μ' obtained by adding an uneven offset value to a quantitative absorption coefficient image is calculated based on optimization Of an evaluation function relating to positron CT measurement data (TOF-PET measurement data) including information on a Time Of Flight (Time Of Flight) Of annihilation radiation. Meanwhile, in step S1, a radiological image λ' is calculated. The reconstruction algorithm in step S1 is the simultaneous reconstruction algorithm described above.

On the other hand, in steps S3, S4, object mask data (i.e., object mask projection data m) in the projection data space is calculated based on the measurement data_proj). In step S5, the image μ is shifted_offEstimating the offset image mu by a reconstruction algorithm in which the forward projection data of (2) is constructed to approximate the subject mask projection data_off。

On the other hand, at least one or more regions Ω are extracted in step S6 using an image that can identify the subject region calculated based on the measurement data.

Here, as described in the section of "means for solving the problem", the "image calculated based on the measurement data and capable of identifying the subject region" is, for example, the image μ 'created in step S2, the radiological image λ' obtained in step S1, an image that is non-quantitative and estimated by a reconstruction algorithm (for example, the ML-EM method) different from the reconstruction algorithm (simultaneous reconstruction algorithm) in step S1, and the subject mask projection data m from the subject mask projection data m_projEstimated object mask image m_img. Of course, the present invention is not limited to these exemplary images, and may be any image that can identify the subject region calculated based on the measurement data. In addition, as also described in the column of "solution to problemThe phrase "at least one or more regions Ω are extracted using an image that can identify a region of a subject calculated based on measurement data" includes not only a case where the region Ω is extracted using a single piece of image information but also a case where the region Ω is extracted using a combination (for example, logical sum or logical product) of a plurality of pieces of image information.

Using the images μ' and the offset images μ obtained in the above-described steps S1 to S6_offAnd region Ω to implement steps S7, S8. In step S7, a coefficient α is calculated that reduces the error between the value of the image μ' within the region Ω and the known absorption coefficient value. Then, in step S8, the offset image μ is added to the value of the image μ' as in the above expression (3)_offMultiplying by a factor alpha times alpha x mu_offThe obtained value was corrected as an absorption coefficient value μ. In this way, the absorption coefficient value is corrected in step S8 based on the mathematical relationship that the difference between the value of the indefinite amount of image μ' in the region Ω and the known absorption coefficient value (the value of the true absorption coefficient image) can be shifted by the offset image μ_offMultiplying by a factor alpha times alpha x mu_offApproximation is performed (that is, μ ≈ μ' + α × μ_off). Thus, the systematic error of the absorption coefficient image having the absorption coefficient value μ corrected in step S8 becomes small. As a result, a quantitative absorption coefficient image can be created, and therefore, accurate absorption correction of the radioactive image can be performed.

In example 1, including examples 2 and 3 described later, steps S1 and S2 corresponding to the reconstruction calculation step described above are performed by a combination of (b) a calculation algorithm including absorption coefficient projection data in an unknown number and an algorithm for reconstructing an image obtained by the absorption coefficient projection data as an image μ'.

(b) The algorithm of (a) is a combination of the MLACF method described in non-patent document 1, which estimates both the non-quantitative radioactive image λ 'and the non-quantitative absorption coefficient projection data (in each of examples 1 to 3, the absorption coefficient sinogram a'), and an algorithm for reconstructing an image obtained by the absorption coefficient projection data (the absorption coefficient sinogram a ') as an image μ'. As described in the section of "means for solving the problem", the algorithm in (b) in which the image obtained by reconstructing the absorption coefficient projection data (absorption coefficient sinogram a ') is used as the image μ' is not particularly limited, and is not limited as long as it is a reconstruction algorithm. In fig. 3, as described in step S2, the absorption coefficient sinogram a 'is reconstructed by the ML-TR method or the ML-EM method to produce an image μ'.

In example 1, steps S3 and S4 corresponding to the mask calculation step described above were performed. That is, the mask calculation step includes the steps of: calculating a binarized image of the image μ' as the subject mask image m_img(step S3); calculating a mask image m of the object_imgThe projection data of (step S4) "projection" of the first half; and calculating a subject mask image m_imgAs the projection data m of the object mask, the binary data of the projection data_proj(the "binarization processing" in the latter half of step S4). The image μ ' is an absorption coefficient image of a variable amount, but as in examples 2 and 3 described later, the image is not an absorption coefficient image (for example, the radiological image λ ' or the radiological image λ ' of example 3)₂') and the projection data are binarized to calculate the subject mask projection data m_proj。

In example 1, the reconstruction process performed in step S5, which corresponds to the offset estimation step, is performed in a calculation method of statistical reconstruction represented by an ML-EM (Maximum Likelihood-expectation maximization) method or the like. Needless to say, the reconstruction processing performed in step S5 is not limited to the statistical reconstruction as in example 1. The reconstruction processing may be performed by any calculation method of analysis reconstruction, statistical reconstruction, and algebraic reconstruction. As the analytical reconstruction, there is, for example, an FBP (Filtered Back Projection) method. As the Algebraic Reconstruction, there is an ART (Algebraic Reconstruction) method, for example.

At least one or more regions Ω extracted in step S6 corresponding to the reference region extraction step described above are regions in which the absorption coefficient can be regarded as a known tissue. Here, as described in the column of "means for solving the problem", the "region of the tissue in which the absorption coefficient can be regarded as known" includes, for example, a region that can be approximated by water, a region that can be approximated by air, a region that can be approximated by brain tissue, a region that can be approximated by bone, a region that can be approximated by lung tissue, a region that can be approximated by soft tissue, and the like. Of course, the present invention is not limited to these exemplified structures, and any structure may be used as long as the approximate value of the absorption coefficient is known. In the case of brain tissue, since it is considered to be a region that can be approximated by water, 0.0096/mm, which is an absorption coefficient value of water, can be used.

In example 1, step S7 corresponding to the coefficient calculation step described above is performed. That is, in example 1, the coefficient α is calculated based on the representative value, including examples 2 to 4 described later. As described above, the representative value is, for example, an average value, a median value, a truncated mean value, a truncated median value, or a weighted average of two or more of these. As described in the section of "solution to problem", the present invention is not limited to these exemplified values, and may be "a statistical amount or a value calculated from the statistical amount".

If image X is replaced by image μ ', S (μ'; Ω)_n) Is the region omega_nIf the image X is replaced by an offset image mu_off', then S (mu)_off；Ω_n) Is the region omega_nIntra offset image mu_off' A representative value. Region omega_nKnown value of the absorption coefficient μⁿ _knownAnd to region omega_nRepresentative value S (μ'; Ω) of the inner image μ_n) Plus make region omega_nIntra offset image mu_off' representative value S (. mu.)_off；Ω_n) Multiplication by the region omega_nInner coefficient alpha_nRear alpha_n×S(μ_off；Ω_n) The obtained values are equal. That is, μⁿ _known＝S(μ'；Ω_n)+α_n×S(μ_off；Ω_n) This is true. Therefore, as shown in the above formula (1), the alpha is represented by_n＝(μⁿ _known-S(μ'；Ω_n))/S(μ_off；Ω_n) Respectively calculate the region omega_nInternal coefficient alpha_n. If K is valued x₁，x₂，…，x_KRespectively substituted by alpha₁，α₂，…，α_KThen T (α)₁，α₂，…，α_K) Is coefficient alpha₁，α₂，…，α_KIs a representative value of (a). In short, each region Ω is calculated by n being 1, …, and K₁，…，Ω_KInner coefficient alpha₁，…，α_KThen, as in the above equation (2), the coefficient α is set₁，…，α_KRepresentative value of (a)₁，α₂，…，α_K) The coefficient α can be calculated by using the coefficient α.

According to the absorption coefficient image estimation program 6 (see fig. 1) of this embodiment 1, by causing a computer (in each embodiment, a GPU, a CPU, or a programmable device constituting the arithmetic circuit 5 shown in fig. 1) to execute the absorption coefficient image estimation program of this embodiment 1, the absorption coefficient value is corrected in step S8 based on a mathematical relationship that is a difference between a value of an indefinite amount of image μ' in the region Ω and a known absorption coefficient value (a value of a real absorption coefficient image) so that the image μ can be shifted by the difference between the values_offMultiplying by a factor alpha times alpha x mu_offAn approximation is made. Thus, the systematic error of the absorption coefficient image having the absorption coefficient value μ corrected in step S8 becomes small. As a result, a quantitative absorption coefficient image can be created, and therefore, accurate absorption correction of the radioactive image can be performed.

According to the PET apparatus 1 (see fig. 1) of the present embodiment 1, by including the arithmetic means (in each embodiment, the GPU, the CPU, or the programmable device constituting the arithmetic circuit 5 shown in fig. 1) for executing the absorption coefficient image estimation program 6 of the present embodiment 1, the absorption coefficient value is corrected in step S8 based on the mathematical relationship that the difference between the value of the indefinite number of images μ' in the region Ω and the known absorption coefficient value (the value of the true absorption coefficient image) can shift the image μ_offMultiplying by a factor alpha times alpha x mu_offAn approximation is made.Thus, the systematic error of the absorption coefficient image having the absorption coefficient value μ corrected in step S8 becomes small. As a result, a quantitative absorption coefficient image can be created, and therefore, accurate absorption correction of the radioactive image can be performed.