阅读说明：本技术 一种小波阈值去噪方法及基于所述方法的光时域反射仪 (Wavelet threshold denoising method and optical time domain reflectometer based on same ) 是由 谭俊 罗惠中 刘偲嘉 甘育娇 崖婷婷 朱铮涛 姜海明 谢康 于 2021-06-04 设计创作，主要内容包括：本发明公开了一种小波阈值去噪方法及基于所述方法的光时域反射仪,包括如下步骤：步骤1：对含噪信号进行小波分解,得到小波分解系数w-(j,k)；步骤2：选取适当的阈值λ-(j)；步骤3：对小波分解系数w-(j,k)进行小波阈值处理,得到估计小波分解系数步骤4：对估计小波分解系数进行重构并得到去噪信号。通过本发明能实现提高信号去噪后的精度,有效提升信号的去噪效果,得到更高的信噪比和更小的均方误差,获得高质量的去噪信号。(The invention discloses a wavelet threshold denoising method and an optical time domain reflectometer based on the method, which comprises the following steps: step 1: wavelet decomposition is carried out on the signal containing the noise to obtain a wavelet decomposition coefficient w j，k (ii) a Step 2: selecting proper threshold value lambda j (ii) a And step 3: for wavelet decomposition coefficient w j，k Performing wavelet threshold processing to obtain estimated wavelet decomposition coefficient And 4, step 4: for estimating wavelet decomposition coefficient And reconstructing to obtain a de-noised signal. The invention can improve the precision of the signal after denoising, effectively improve the denoising effect of the signal, obtain higher signal-to-noise ratio and smaller mean square error, and obtain a high-quality denoised signal.)

1. A wavelet threshold denoising method is characterized in that: the method comprises the following steps:

step 1: wavelet decomposition is carried out on the signal containing the noise to obtain a wavelet decomposition coefficient w_j，k；

Step 2: selecting proper threshold value lambda_j；

And step 3: for wavelet decomposition coefficient w_j，kPerforming wavelet threshold processing to obtain estimated wavelet decomposition coefficient

And 4, step 4: for estimating wavelet decomposition coefficientAnd reconstructing to obtain a de-noised signal.

2. The wavelet threshold denoising method of claim 1, wherein: in step 1, w_j，kIs the kth wavelet coefficient at the jth scale of the decomposition.

3. The wavelet threshold denoising method of claim 2, wherein: in the step 2, the process is carried out,wherein N is_jIs the length of the wavelet decomposition coefficient of the j-th layer, sigma_jIs the standard deviation, σ, of the noise contained in the j-th layer_j＝Median(|w_j，k|)/0.6745。

4. The wavelet threshold denoising method of claim 3, wherein: in the step 3, the process is carried out,

wherein n and m are regulating factors which are positive integers;

5. an optical time domain reflectometer based on the wavelet threshold denoising method of any one of claims 1-4, characterized by: the device comprises a pulse generator, a laser driving module, an optical fiber coupler, a photoelectric conversion module, an A \ D conversion module and a microcontroller module which are connected in sequence; the microcontroller module is connected with the threshold denoising module.

6. An optical time domain reflectometry according to claim 5, wherein: the threshold denoising module comprises a wavelet decomposition module, a threshold selecting module, a threshold processing module and a signal reconstruction module which are connected in sequence.

Technical Field

The invention relates to the technical field of optical fiber testing, in particular to a wavelet threshold denoising method and an optical time domain reflectometer based on the method.

Background

An Optical Time Domain Reflectometer (OTDR) is a non-destructive testing instrument designed according to the transmission characteristics of Optical fiber, and is one of the main instruments in Optical fiber testing. The device can be used for testing the equivalent of the length of the optical fiber, the transmission attenuation of the optical fiber and the attenuation of a joint, has the advantages of distributed measurement, remote measurement, high sensitivity, strong anti-electromagnetic interference capability, good insulativity, light weight, small volume and the like, and is widely applied to the aspects of construction, maintenance, operation and the like of the communication optical fiber and the sensing optical fiber. However, the actual OTDR test curve contains a lot of noise, especially at the tail of the curve, because the attenuation of the optical power is large, the curve is seriously polluted by the noise, and the events in the curve are difficult to identify. Noise is an important factor influencing the detection and identification performance of a target signal, and particularly in the analysis of some high-precision data, even very weak noise can have a great influence on an analysis result, so in the signal analysis process, the signal is subjected to denoising processing. Wavelet analysis is a new signal processing tool developed in recent years, and this method is derived from fourier analysis. Wavelets (wavelets), i.e. waves of a small area, have non-zero values only for a very limited section of the interval, rather than being endless as sine and cosine waves do. The wavelet can be translated back and forth along a time axis, and can also be stretched and compressed in proportion to obtain low-frequency wavelets and high-frequency wavelets, and the constructed wavelet function can be used for filtering or compressing signals, so that useful signals in the signals containing noise can be extracted, and therefore the wavelet theory is developed very rapidly. The commonly used wavelet denoising methods include: wavelet threshold denoising, wavelet correlation denoising, and wavelet modulus maximum denoising. Wavelet threshold denoising was proposed by d.l.donoho and i.m.johnstone in 1992, and the basic idea of the method is: after wavelet decomposition, the energy of signal itself exists in partial wavelet decomposition coefficient, and the energy of noise is distributed in all wavelet decomposition coefficients, after multi-layer wavelet decomposition, the wavelet coefficient module value of signal itself is greater than the coefficient module value of noise signal wavelet transformation, and then threshold processing and wavelet reconstruction are carried out to obtain the de-noised signal. Among all wavelet denoising methods, the wavelet threshold denoising method is the most widespread, and has become one of the research hotspots in the signal denoising field in recent years.

The functions applied by the traditional wavelet threshold denoising method include a hard threshold function and a soft threshold function, but both methods have certain defects: the hard threshold function is discontinuous at the threshold, so that the reconstructed signal has oscillation and pseudo Gibbs effect; although the soft threshold function is continuous at the threshold, a constant deviation exists between the processed wavelet coefficient and the real wavelet coefficient, so that the reconstruction precision of the wavelet coefficient is reduced, and the denoising effect is poor. In order to overcome the defects of the soft threshold function and the hard threshold function, researchers at home and abroad propose a ratio smoothing threshold function. The ratio smoothing threshold function is continuous at the threshold, and can also solve the problem of poor denoising effect of the soft threshold function to a certain extent, but the signal-to-noise ratio and the mean square error obtained by denoising of the function are not ideal compared with the hard threshold function.

The functional form and image of the above three methods are as follows.

(1) Hard threshold function:

(2) soft threshold function:

(3) ratio smoothing threshold function:

wherein, w_j，kFor the kth wavelet coefficient at the jth scale of the decomposition,is w_j，kThe estimated wavelet coefficients, n being the adjustment factor, are a positive integer,p＝(e^λ+e^-λ) A/2, where λ is a threshold value,n is the length of the signal, σ_nIs the standard deviation, σ, of the noise contained in layer 1_n＝Median(|w_1，k|)/0.6745。

The soft threshold function, the hard threshold function, and the ratio smoothing threshold function are shown in fig. 1.

Disclosure of Invention

The invention aims to design a wavelet threshold denoising method and an optical time domain reflectometer based on the method, so that the method can improve the precision of the denoised signal, effectively improve the denoising effect of the signal, obtain higher signal-to-noise ratio and smaller mean square error, and obtain a high-quality denoised signal.

In order to achieve the above object, the present invention claims a wavelet threshold denoising method, comprising the following steps:

step 1: wavelet decomposition is carried out on the signal containing the noise to obtain a wavelet decomposition coefficient w_j，k；

Step 2: selecting proper threshold value lambda_j(ii) a In the actual denoising process, after a noisy signal is subjected to wavelet decomposition, along with the increase of the scale, the amplitude of the wavelet coefficient of the noise is smaller and smaller, and the amplitude of the wavelet coefficient of the signal is larger and larger. Therefore, the selection of the threshold value should be different on different scales, so that the threshold value can adapt to the noise distribution condition of each layer;

and step 3: for wavelet decomposition coefficient w_j，kPerforming wavelet threshold processing to obtain estimated wavelet decomposition coefficient

And 4, step 4: for estimating wavelet decomposition coefficientAnd reconstructing to obtain a de-noised signal.

Specifically, in step 1, w_j，kIs the kth wavelet coefficient at the jth scale of the decomposition.

Specifically, in step 2, the first step,wherein N is_jIs the length of the wavelet decomposition coefficient of the j-th layer, sigma_jIs the standard deviation, σ, of the noise contained in the j-th layer_j＝Median(|w_j，k)/0.6745. It can be seen that as the decomposition scale j becomes larger, the threshold value becomes smaller, which is in accordance with the characteristic that the amplitude of the noise becomes smaller as the decomposition scale becomes larger.

Specifically, in step 3,

wherein n and m are regulating factors which are positive integers;

the invention also claims an optical time domain reflectometer based on the wavelet threshold denoising method, which comprises a pulse generator, a laser driving module, an optical fiber coupler, a photoelectric conversion module, an A \ D conversion module and a microcontroller module which are connected in sequence; the microcontroller module is connected with the threshold denoising module.

A pulse generator, mainly comprising electronic circuitry for generating electrical pulses corresponding to the optical pulses required for the OTDR measurements; the laser driving module is used for converting the electric pulse generated by the pulse generator into an optical pulse and transmitting the optical pulse to the optical fiber coupler through an optical fiber; the optical fiber coupler transmits the optical pulse to the optical fiber to be detected through the optical fiber so as to facilitate the detection feedback of an operator, and simultaneously transmits the optical pulse reflected in the optical fiber to be detected to the photoelectric conversion module for detection; the photoelectric conversion module receives a light signal to be measured and converts the light signal into an analog electric signal; the A \ D conversion module converts the analog electric signal into a digital electric signal and then sends the digital electric signal to the microcontroller module for processing; the microcontroller module stores the data of the noisy signals sent from the A \ D conversion module by using a memory, then transmits the data to the threshold denoising module through a bus, and controls the working process of the threshold denoising module.

Specifically, the threshold denoising module comprises a wavelet decomposition module, a threshold selecting module, a threshold processing module and a signal reconstruction module which are connected in sequence.

The wavelet decomposition module selects a proper wavelet basis function, performs wavelet decomposition on the noise-containing signal, and obtains a series of low-frequency wavelet coefficients and high-frequency wavelet coefficients after decomposition; the low-frequency wavelet coefficient is kept unchanged, and the high-frequency wavelet coefficient enters a threshold selection module to select a proper threshold; the threshold processing module processes by using the wavelet threshold function; and the signal reconstruction module combines the processed high-frequency wavelet coefficient and the low-frequency wavelet coefficient to reconstruct the OTDR signal.

Compared with the prior art, the invention has the beneficial effects that:

compared with the traditional hard threshold function, soft threshold function and ratio smooth threshold function, the wavelet threshold function applied by the wavelet threshold denoising method can obtain better signal-to-noise ratio and smaller mean square error for denoising the noise-containing signal, and effectively improve the quality of the denoised signal.

The optical time domain reflectometer based on the wavelet threshold denoising method can effectively detect the optical fiber and improve the detection effect under the mutual cooperation of the pulse generator, the laser driving module, the optical fiber coupler, the photoelectric conversion module, the A \ D conversion module, the microcontroller module and the threshold denoising module.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a comparison graph of soft threshold function, hard threshold function, and ratio smoothing threshold function;

FIG. 2 is a graph comparing a wavelet threshold function with a soft threshold function and a hard threshold function of the present invention;

FIG. 3 is a schematic structural diagram of an optical time domain reflectometer of the present invention;

FIG. 4 is a schematic structural diagram of a threshold denoising module according to the present invention;

Detailed Description

The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and obviously, the description is only a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.

A wavelet threshold denoising method comprises the following steps:

step 1: wavelet decomposition is carried out on the signal containing the noise to obtain a wavelet decomposition coefficient w_j，k；

Step 2: selecting proper threshold value lambda_j(ii) a In the actual denoising process, after a noisy signal is subjected to wavelet decomposition, along with the increase of the scale, the amplitude of the wavelet coefficient of the noise is smaller and smaller, and the amplitude of the wavelet coefficient of the signal is larger and larger. Therefore, the selection of the threshold value should be different on different scales, so that the threshold value can adapt to the noise distribution condition of each layer;

and step 3: for wavelet decomposition coefficient w_j，kGo to smallWave threshold processing to obtain estimated wavelet decomposition coefficient

And 4, step 4: for estimating wavelet decomposition coefficientAnd reconstructing to obtain a de-noised signal.

Specifically, in step 1, w_j，kIs the kth wavelet coefficient at the jth scale of the decomposition.

Specifically, in step 2, the first step,wherein N is_jIs the length of the wavelet decomposition coefficient of the j-th layer, sigma_jIs the standard deviation, σ, of the noise contained in the j-th layer_j＝Median(|w_j，k)/0.6745. It can be seen that as the decomposition scale j becomes larger, the threshold value becomes smaller, which is in accordance with the characteristic that the amplitude of the noise becomes smaller as the decomposition scale becomes larger.

Specifically, in step 3,

wherein n and m are regulating factors which are positive integers;

an optical time domain reflectometer based on the wavelet threshold denoising method comprises a pulse generator, a laser driving module, an optical fiber coupler, a photoelectric conversion module, an A \ D conversion module and a microcontroller module which are connected in sequence; the microcontroller module is connected with the threshold denoising module.

A pulse generator, mainly comprising electronic circuitry for generating electrical pulses corresponding to the optical pulses required for the OTDR measurements; the laser driving module is used for converting the electric pulse generated by the pulse generator into an optical pulse and transmitting the optical pulse to the optical fiber coupler through an optical fiber; the optical fiber coupler transmits the optical pulse to the optical fiber to be detected through the optical fiber so as to facilitate the detection feedback of an operator, and simultaneously transmits the optical pulse reflected in the optical fiber to be detected to the photoelectric conversion module for detection; the photoelectric conversion module receives a light signal to be measured and converts the light signal into an analog electric signal; the A \ D conversion module converts the analog electric signal into a digital electric signal and then sends the digital electric signal to the microcontroller module for processing; the microcontroller module stores the data of the noisy signals sent from the A \ D conversion module by using a memory, then transmits the data to the threshold denoising module through a bus, and controls the working process of the threshold denoising module.

Specifically, the threshold denoising module comprises a wavelet decomposition module, a threshold selecting module, a threshold processing module and a signal reconstruction module which are connected in sequence.

The wavelet decomposition module selects a proper wavelet basis function, performs wavelet decomposition on the noise-containing signal, and obtains a series of low-frequency wavelet coefficients and high-frequency wavelet coefficients after decomposition; the low-frequency wavelet coefficient is kept unchanged, and the high-frequency wavelet coefficient enters a threshold selection module to select a proper threshold; the threshold processing module processes by using the wavelet threshold function; and the signal reconstruction module combines the processed high-frequency wavelet coefficient and the low-frequency wavelet coefficient to reconstruct the OTDR signal.

The soft threshold function, the hard threshold function, and the wavelet threshold function pair of the present invention are shown in fig. 4.

In order to verify the denoising effectiveness of the system, a soft threshold function method, a hard threshold function method, a ratio smoothing threshold function method and the wavelet threshold function method are respectively adopted in a threshold denoising module of the system to carry out simulation experiments. The noise-containing signal is subjected to wavelet decomposition with the scale of 6 by adopting the Sym6 wavelet basis, and adjustment factors n and m in the improved threshold function are respectively 3 and 1. The signal-to-noise ratio (SNR) and mean square error (RMSE) obtained by the 4 methods are shown in table 1.

TABLE 1 comparison of SNR and RMSE after denoising with different threshold functions

As can be seen from Table 1, the system of the present invention can effectively improve the signal-to-noise ratio of the signal, and the amplitude of the improvement of the signal-to-noise ratio is greater than that of the hard threshold method, the soft threshold method and the ratio smoothing threshold method. In addition, the mean square error of the method is reduced compared with a hard threshold method, a soft threshold method and a ratio smooth threshold method, and the result is superior to other denoising systems.