CN111932473A - Phase information noise reduction algorithm of multi-resolution sparse coding and storage medium - Google Patents

Abstract

The invention discloses a phase information noise reduction algorithm of multiresolution sparse coding and a storage medium, and provides a phase image noise reduction technology based on multiresolution sparse coding in a complex domain by realizing a multiresolution adaptive dictionary training algorithm in the complex domain according to the self-similarity and multiresolution similarity of interference phase images, thereby improving the noise reduction effect of the complex phase and laying a foundation for realizing phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in magnetic resonance images.

Description

A phase information noise reduction algorithm and storage medium for multi-resolution sparse coding

technical field

The present invention relates to the technical field of interferometry in complex number domain, in particular to a multi-resolution sparse coding phase information noise reduction algorithm and a computer-readable storage medium.

Background technique

At present, phase images in the complex domain are widely used in practical measurements. For example, terrain elevation can be measured by interferometry of synthetic aperture radar. The SRTM system of the US space shuttle radar terrain mapping mission uses this measurement method to obtain global digital elevation data. Changes in terrain due to earthquakes or resource development can also be measured by interferometry. In the medical field, complex MRI images guide diagnosis through complex phase images.

However, whether using synthetic aperture radar interferometry or nuclear magnetic resonance image measurement, due to the inherent factors of the measurement equipment and the interference of the measurement environment, there is noise in the final complex measurement image, which affects the measurement accuracy, and It may cause subsequent processing to fail. Therefore, how to achieve denoising has become an urgent problem to be solved.

SUMMARY OF THE INVENTION

The present invention provides a multi-resolution sparse coding phase information noise reduction algorithm and a computer-readable storage medium, so as to solve the problem in the prior art that the measurement accuracy is affected by the existence of noise in the complex measurement image.

In a first aspect, the present invention provides a multi-resolution sparse coding phase information noise reduction algorithm, the method comprising: acquiring complex multi-resolution images corresponding to phase images to be denoised, and dividing each resolution image into image blocks respectively Obtaining a set of image blocks, wherein there are multiple sets of image blocks, and the sets of image blocks are uniquely corresponding to the resolution images respectively; respectively perform the following steps for any set of image blocks: the image blocks in the image block set, obtain a coding dictionary through online training, encode the image block set through the coding dictionary, obtain sparse coding coefficients corresponding to the image block set, and use the coding dictionary Multiplying the sparse coding coefficients to obtain image blocks after noise reduction, and combining the set of image blocks according to the inverse operation of segmentation to obtain a noise-reduced image; fuse the noise-reduced images of different resolutions , obtain the final complex phase image after noise reduction, and obtain the final phase noise reduction result by taking the complex phase operation.

Optionally, the acquiring a complex multi-resolution image corresponding to the phase image to be denoised includes:

The phase image to be denoised is converted into a resolution image corresponding to a complex number by z=e ^jφ , wherein φ is the phase image to be denoised, e is a natural base, and j is an imaginary unit;

According to the number of multi-resolution layers to be acquired, the two-dimensional Harr wavelet transform method is used to obtain complex images z ⁽¹⁾ , z ⁽²⁾ ,...z ^(R) of different resolutions to be denoised, where R is the resolution layers.

Optionally, the multi-resolution images are divided into image blocks to obtain image block sets, including:

其中，N_p为图像z能够分割的图像块个数，T为转置；Convert the complex images z ⁽¹⁾ , z ⁽²⁾ ,...z ^(R) to be denoised into column vectors according to the column-by-column splicing method. According to the size of the divided image blocks, firstly, the corresponding vectors of the original image are divided into image blocks, Define the selection matrix M _i such that _zi = M _i z, each row of the matrix M _i has only one non-zero element and its value is 1, where zi _i is the ith image block; define the following matrix

Among them, N _p is the number of image blocks that the image z can be divided into, and T is the transposition;

的图像块的集合，m一般取整数的平方，如81，100等，即：Similarly, for z ⁽¹⁾ , z ⁽²⁾ ,…z ^(R) of different resolutions, define the corresponding partition matrices M ⁽¹⁾ , M ⁽²⁾ ,…M ^(R) respectively. The original image corresponding vector is divided into a size of

The set of image blocks, m generally takes the square of the integer, such as 81, 100, etc., namely:

Optionally, a coding dictionary is obtained through online training for the complex-numbered image blocks corresponding to the phase image to be denoised, including:

中随机获取图像块组z^t,t＝1,…,N_g，N_g为所选择的图像块组中图像块的个数，按照预定顺序根据所述图像块组进行词典学习，训练的每一个循环采用其中的一个图像块组进行字典元素更新，即通过最小化下式进行字典训练：from the collection

Randomly obtain image block groups z ^t , t=1,...,N _g , where N _g is the number of image blocks in the selected image block group, and perform dictionary learning according to the image block groups in a predetermined order. A loop uses one of the image block groups to update dictionary elements, that is, dictionary training by minimizing the following formula:

Optionally, the step of obtaining the encoding of the multi-resolution image block set includes:

中的每一个向量z_i进行稀疏编码通过求解下面的最优化问题来获得For the image block set at each resolution, the column vector corresponding to each image block in the image block set is sparsely encoded. For the dictionary D obtained by training, if the

Each vector z _i in the sparse coding is obtained by solving the following optimization problem

来获得最优化编码。α_i是z_i在字典D的编码，

是

在字典D上的编码。For resolution r, by solving

to get the optimal encoding. α _i is the encoding of _zi in dictionary D,

Yes

encoding on dictionary D.

Optionally, multiplying the coding dictionary with the sparse coding coefficients to obtain image blocks after noise reduction, including:

为z_i降噪后图像块，

为

降噪后图像块。Among them, N _r is the number of image blocks of the rth resolution,

is the image block after denoising for z _i ,

for

Image block after noise reduction.

Optionally, the image block set is assembled according to the inverse operation of the segmentation to obtain denoised images at different resolutions, including:

The image block sets under the same resolution are combined according to the following formula to obtain denoised images under different resolutions;

是z的降噪结果，

是z^(r)的降噪结果in,

is the noise reduction result of z,

is the noise reduction result of z ^(r)

Optionally, the denoised images of different resolutions are fused to obtain a final complex denoising effect, including:

According to the order from high resolution to low resolution, the final fusion result is obtained by means of hypothesis testing, and the fusion result of each step is used as the fusion input of the next resolution;

进行上采样，获取与

同样大小N₁×N₂的降噪结果，N₁为

的长，N₂为

的宽，假设如下：First put

Upsampling is performed to obtain the

The noise reduction results of the same size N ₁ × N ₂ , N ₁ is

The length of _N2 is

width, assuming the following:

服从零均值高斯分布，高斯分布的标准差为σ，则在置信度为0.95的情况下，对于图像中的每一个像素点，应当满足如下条件Assumption

It obeys the zero-mean Gaussian distribution, and the standard deviation of the Gaussian distribution is σ, then when the confidence level is 0.95, for each pixel in the image, the following conditions should be met

是可用的，反之，则可以认为估计不可用，因此将

和

的融合结果为If the above formula is satisfied, it is considered that when the resolution is r=1, it is estimated that

is available, otherwise, it can be considered that the estimate is not available, so the

and

The fusion result is

where i=1,2,...,N ₁ ,j=1,2,...,N ₂ ;

进行融合得到zr₂，并得到与最后一级分辨率R的降噪结果的融合结果zr_R。Similarly, according to the above method, zr ₁ and

Perform fusion to obtain zr ₂ , and obtain a fusion result zr _R with the noise reduction result of the last-level resolution R.

Optionally, obtaining the final phase noise reduction result by taking the complex phase operation, including:

According to the fusion result zr _R of the final complex number image, the phase angle of the complex number zr _R is obtained as the estimated value of the final phase:

其中imag(·)和real(·)分别为计算实部和虚部。

where imag( ) and real( ) are the real and imaginary parts of the calculation, respectively.

In a second aspect, the present invention provides a computer-readable storage medium, characterized in that, the computer-readable storage medium stores a computer program for signal mapping, and when the computer program is executed by at least one processor, the above-mentioned computer program is implemented. Any one of the multi-resolution sparse coding phase information noise reduction algorithms.

The beneficial effects of the present invention are as follows:

According to the self-similarity and multi-resolution similarity of the interference phase image, the invention proposes a phase image noise reduction based on multi-resolution sparse coding in the complex number domain through the realization of the multi-resolution adaptive dictionary training algorithm in the complex number domain. technology to improve the noise reduction effect of complex phase, thus laying the foundation for phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in magnetic resonance images.

Description of drawings

1 is a schematic flowchart of a phase information noise reduction algorithm for multi-resolution sparse coding provided by an embodiment of the present invention;

2 is a schematic flowchart of another multi-resolution sparse coding phase information noise reduction algorithm provided by an embodiment of the present invention;

3 is a schematic diagram of a phase information noise reduction algorithm for multi-resolution sparse coding provided by an embodiment of the present invention;

FIG. 4 is a schematic diagram of sparse coding provided by an embodiment of the present invention.

Detailed ways

With the development of signal transform theory, especially the proposal of discrete Fourier transform, discrete cosine transform and discrete wavelet transform, it plays an important role in the noise reduction of discrete signals in computer systems. The essence of these algorithms is sparse coding, which shows that natural signals can be represented by a small number of elements in a representation base (also known as a dictionary). The basic principle of using sparse coding for noise reduction is that the signal space is included in the observation space of the signal, and the dictionary in the sparse coding technique should be the support base of the signal space, but not the support base of the signal observation space. In other words, the signal observation space contains both signal and noise. A good dictionary can sparsely encode the signal, but cannot sparsely encode the noise. Through the encoding and decoding process, the noise in the observation signal can be effectively filtered out, and then To achieve the purpose of removing noise and improving accuracy. Through the above analysis, it can be concluded that in order to realize the signal noise reduction problem based on sparse coding, it is necessary to have an excellent representation dictionary first, and secondly, to be able to perform effective encoding and decoding processes. Therefore, the present invention focuses on patent application and maintenance in these three aspects.

When sparse coding was first proposed, the dictionary was fixed, for example in discrete cosine transforms decomposing the signal by cosine basis. However, a fixed representation base cannot obtain a higher sparsity, and cannot obtain a better noise reduction or compression effect. However, the representation dictionary obtained by training the signal to be represented has better adaptability, so it can obtain more satisfactory representation results. Some intelligent algorithms have been proposed for training adaptive dictionaries. A redundant representation-based K-SVD algorithm is proposed for image denoising, in which the representation dictionary is trained from image patches extracted from noisy images. Later, the algorithm was extended to the 3D domain to solve the inpainting problem of color images. Some researchers have improved the dictionary training algorithm by random approximation and used it in large data with millions of training samples. In 2012, a general approach to supervised dictionary training algorithms was proposed for different classes of tasks. Later dictionaries also began to gradually adapt to group sparse coding, that is, similar signal blocks should have similar coding based on the same coding dictionary, or the coding has the same characteristics.

Regarding the encoding and decoding problems, in order to realize that the encoding algorithm can better encode the signal and avoid encoding the noise, the representation dictionary obtained by general training is a redundant dictionary, so the encoding of the signal is sparse, that is, a small amount of encoding The elements of is non-zero, and most of the elements in the encoded vector are 0. In the actual encoding process, the zero-norm regularization method is generally used to realize the constraint on the number of zero elements. However, in the encoding optimization problem, the optimization problem obtained by using the zero-norm regularization method is non-convex, so it is necessary to relax the problem into a convex optimization problem or use a greedy algorithm to solve the encoding of the observed signal. After the sparse coding is obtained, the original signal can be restored through the coding dictionary and sparse coding. Since the coding of noise is avoided in the sparse coding process, the interference of noise will be filtered out after restoration, thereby realizing noise reduction.

Among the algorithms for denoising complex-valued phase information using sparse coding, there are currently three types of important algorithms: one is to denoise the phase image directly through sparse coding technology. Truncated in the interval [-π,π), the effect of this type of algorithm is not very ideal. The noise reduction algorithm filters out the details of the signal while filtering out the noise, which reduces the accuracy of the signal. The second type of algorithm is to denoise the real part and imaginary part of the complex value through sparse coding technology, fuse the noise reduction results of the two parts to obtain the denoised complex value, and obtain the phase of the complex value as the original complex value. The noise reduction result of the phase information in the value. The main disadvantage of this type of algorithm is that the real and imaginary parts of complex numbers are processed separately, ignoring the correlation between the real and imaginary parts, resulting in the final phase noise reduction result accuracy value still has room for improvement. The third type of algorithm is to denoise the complex value as a whole through sparse coding technology. This type of algorithm fully considers the correlation between the real part and the imaginary part of the complex number. The noise reduction phase obtained by denoising the complex number Can achieve better noise reduction effect. The algorithm proposed by the present invention belongs to the third type of noise reduction algorithm. The difference between the algorithm of the present invention and the previous algorithm is that noise reduction is realized by means of multi-resolution dictionary training and sparse coding, thereby further improving the noise reduction effect of the phase image.

The purpose of the embodiment of the present invention is to propose a multi-resolution sparse coding based multi-resolution sparse coding method in the complex number domain through the realization of the multi-resolution adaptive dictionary training algorithm in the complex number domain according to the self-similarity and the multi-resolution similarity of the interference phase image. The phase image noise reduction technology improves the noise reduction effect of complex phases, thereby laying the foundation for phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in magnetic resonance images. In the present invention, a two-dimensional wavelet transform method is used to obtain the complex multi-resolution form of the phase image to be denoised, and the obtained multi-resolution images are divided into image blocks to obtain an image block set. Then, the complex coding dictionary is obtained by using the online training method corresponding to the complex image blocks of the original phase image, and the sparse coding coefficients are obtained by encoding the multi-resolution image block set using the dictionary obtained by training. The denoised image block is obtained by multiplying the coding dictionary and the coding coefficients. The image block sets are assembled according to the inverse operation of the segmentation method to obtain the noise reduction results under different resolutions, the noise reduction results of different resolutions are fused to obtain the final complex noise reduction effect, and the complex number is obtained by taking the phase operation to obtain the final phase. Noise reduction results.

During specific implementation, the phase information noise reduction algorithm of multi-resolution sparse coding according to the embodiment of the present invention, referring to FIG. 1 , includes:

S101. Acquire complex multi-resolution images corresponding to the phase image to be denoised, and perform image block segmentation on each resolution image to obtain an image block set, wherein the image block sets are multiple, and the image block sets are The resolution images are uniquely corresponding;

S102. Perform the following steps on any of the image block sets: obtaining a coding dictionary for the image blocks in the image block set through online training, and encoding the image block set by using the coding dictionary to obtain the sparse coding coefficients corresponding to the set of image blocks, and multiplying the coding dictionary with the sparse coding coefficients to obtain image blocks after noise reduction, and stitching the set of image blocks according to the inverse operation of segmentation, Get the denoised image;

S103 , fuse the denoised images of different resolutions to obtain a final complex denoised phase image, and obtain a final phase denoising result by taking the complex phase operation.

That is to say, the embodiment of the present invention is aimed at the noise interference problem of the phase image, and uses the multi-resolution sparse coding technology to encode the signal, but cannot encode random noise. Through the coding and decoding process and method design, the noise in the complex measurement signal is filtered, the accuracy of the phase information in the complex measurement signal is improved, and the foundation for later signal applications is laid.

The method described in the present invention will be explained and described in detail below with reference to Fig. 2 and Fig. 3 through a specific example:

In the embodiment of the present invention, the acquisition of the multi-resolution image block set specifically includes:

(a) Multi-resolution complex image acquisition:

If the complex image z corresponding to the phase image is provided for phase noise reduction, then operate it directly; if the noisy phase image φ is provided for phase noise reduction, use

z=e ^jφ Formula 1

Convert to complex numbers and do the following.

According to the number of multi-resolution layers to be acquired, the two-dimensional Harr wavelet transform method is used to obtain complex images z ⁽¹⁾ , z ⁽²⁾ ,...z ^(R) of different resolutions to be denoised, among which the low resolution The image only takes the low frequency resolution after wavelet transformation. Because it is obtained by two-dimensional wavelet transform, the length and width of the next-level resolution image are both half of those of the previous-level resolution image.

(b) Multi-resolution image patch segmentation:

Convert the image matrices z, z ⁽¹⁾ , z ⁽²⁾ ,...z ^(R) into column vectors in a column-by-column stitching manner. According to the size of the divided image block, firstly, the corresponding vector of the original image is divided into image blocks, and the selection matrix M _i is defined so that _zi = M _i z (each row of the matrix M _i has only one non-zero element and its value is 1), where z _i is the ith image block. Define the following matrix

的图像块，则分割的个数为

Among them, N _p is the number of image blocks that the image z can be divided into. For example, for an image z of size N=N ₁ ×N ₂ , to be divided into

image blocks, the number of divisions is

的图像块的集合，即Similarly, for z ⁽¹⁾ , z ⁽²⁾ ,…z ^(R) of different resolutions, define partition matrices M ⁽¹⁾ , M ⁽²⁾ ,…M ^(R) . By selecting the matrix, the original image corresponding vector can be divided into the size of

a collection of image blocks, i.e.

训练得到稀疏编码字典，采用字典训练算法获取自适应词典的目的是能够需找到一个编码字典，运用其中的较少数目字典原子的线性组合就可以实现对训练集中图像块的表示，其训练过程可以通过下面的最优化问题进行描述。The training of the coding dictionary in the embodiment of the present invention specifically includes: according to the set

The sparse coding dictionary is obtained by training, and the purpose of using the dictionary training algorithm to obtain the adaptive dictionary is to find a coding dictionary, and use the linear combination of a small number of dictionary atoms to realize the representation of the image blocks in the training set. The training process can be It is described by the following optimization problem.

其中前面的一项为表示误差，后面的一项为稀疏约束项，两项通过正则化参数λ＞0来进行平衡。约束条件D∈C是为了防止字典中的元素趋于任意大。在式(5)中，后一项稀疏约束是通过L1范数来进行约束的，这是因为在实际的实验中，L1范数方式获取的编码字典对于复数的降噪具有更好的效果。in

The former term is the representation error, the latter term is the sparse constraint term, and the two terms are balanced by the regularization parameter λ>0. The constraint D∈C is to prevent the elements in the dictionary from tending to be arbitrarily large. In Equation (5), the latter sparse constraint is constrained by the L1 norm, because in the actual experiment, the coding dictionary obtained by the L1 norm method has a better effect on the denoising of complex numbers.

分别进行最优化求解。对D最优化求解是一个凸集上的二次优化问题，对

最优化是凸优化问题且可分解的。最优化问题式5对于字典D求最优化问题相对较简单，但是对于编码

最优化求解非常耗时。为了提高计算效率，降低字典训练的解决这个问题，本发明采用在线词典训练方法。首先从集合

中随机获取图像块组z^t,t＝1,…,N_g，然后按照一定顺序根据这些图像块组进行词典学习。训练的每一个循环采用其中的一个图像块组进行字典元素更新。即通过最小化下式进行字典训练。The usual way to solve Equation 5 is to interactively encode the dictionary D and

The optimization solutions are carried out separately. The optimal solution to D is a quadratic optimization problem on a convex set.

The optimization is a convex optimization problem and decomposable. The optimization problem Equation 5 is relatively simple to find the optimization problem for the dictionary D, but for the encoding

The optimization solution is very time consuming. In order to improve computing efficiency and reduce dictionary training to solve this problem, the present invention adopts an online dictionary training method. First from the collection

Randomly obtain image block groups z ^t , t=1, . . . , N _g , and then perform dictionary learning according to these image block groups in a certain order. Each loop of training uses one of the image block groups to update dictionary elements. That is, dictionary training is performed by minimizing the following equation.

In the embodiment of the present invention, the encoding for acquiring the multi-resolution image block set specifically includes:

中的每一个向量z_i进行稀疏编码通过求解下面的最优化问题来获得For the image block set at each resolution, sparse coding is performed on the column vector corresponding to each image block in the image block set, as shown in FIG. 4 . For the dictionary D obtained by training, if the

Each vector z _i in the sparse coding is obtained by solving the following optimization problem

For the resolution r, it can be obtained by solving the following optimization problem.

The above optimization problem can be solved using a greedy algorithm.

The fusion of multi-resolution image blocks in the embodiment of the present invention specifically includes:

(a) Acquisition of multi-resolution complex image denoised image blocks:

Through the above steps, we have obtained the sparse coding dictionary D and the codes at various resolutions. The noise reduction results of the segmented image blocks can be obtained by multiplying the coding dictionary with the sparse coding.

which is

(b) Flattening of image patch sets:

After obtaining the noise reduction set of image blocks, the inverse operation of image block segmentation is performed for multiple resolutions, and the image blocks under the same resolution are combined into a whole image. The stitching process is the inverse operation of Equation 3 and Equation 4.

以及对应于分辨率r的降噪估计结果

在本发明下面的步骤中是如何将

以及不同分辨率的降噪结果

进行融合，得到最终的降噪结果。这是本发明重点维护的部分。Through the above operations, the complex noise reduction estimation result corresponding to the original phase image is obtained

and the noise reduction estimation result corresponding to the resolution r

In the following steps of the present invention, how

and noise reduction results at different resolutions

Fusion is performed to obtain the final noise reduction result. This is the important maintenance part of the present invention.

(c) Fusion of multi-resolution noise reduction results:

In the fusion process of noise reduction results of different resolutions, the present invention adopts a hypothesis test method from high resolution to low resolution to obtain the final fusion result. The fusion result of each step is used as the fusion input for the next resolution.

和

首先将

进行上采样，获取与

同样大小N₁×N₂的降噪结果，。假设如下：first look

and

First put

Upsampling is performed to obtain the

The noise reduction results of the same size N ₁ × N ₂ , . Suppose the following:

服从零均值高斯分布，高斯分布的标准差为σ，则在置信度为0.95的情况下，对于图像中的每一个像素点，应当满足如下条件It can be assumed

It obeys the zero-mean Gaussian distribution, and the standard deviation of the Gaussian distribution is σ, then when the confidence level is 0.95, for each pixel in the image, the following conditions should be met

是可用的，反之，则可以认为估计不可用，因此将

和

的融合结果为If Equation 14 is satisfied, it can be considered that when the resolution is r=1, it is estimated that

is available, otherwise, it can be considered that the estimate is not available, so the

and

The fusion result is

进行融合得到zr₂，如此继续得到与最后一级分辨率R的降噪结果的融合结果zr_R。where i=1,2,...,N1,j= _1,2 ,..., _N2 . The following applies the same method to zr ₁ to

Perform fusion to obtain zr ₂ , and then continue to obtain the fusion result zr _R with the noise reduction result of the last-level resolution R.

(d) Obtain the phase image noise reduction results:

According to the fusion result zr _R of the final complex number image, the phase angle of the complex number zr _R is obtained, which is the estimated value of the final phase.

where imag( ) and real( ) are the real and imaginary parts of the calculation, respectively.

The main point of the method of the present invention is to use the hypothesis testing method to fuse the multi-resolution noise reduction results, that is, the calculation method of Equation 15. Before the fusion of the noise reduction results, the wavelet transform is used to perform multi-resolution decomposition, and the training of the sparse coding dictionary is performed by using the formula 6, and the sparse coding is performed by using the formula 7 and formula 8. Finally, the inverse operation of the block will reduce the The denoised blocks are merged to obtain denoising results at different resolutions.

The method of the present invention mainly performs the following steps:

(1) Convert the input phase image into a complex number form. If its amplitude is known, take it as a complex amplitude value. If no amplitude value is input, set the amplitude to 1, and use the wavelet transformation method to obtain different phase images. Resolution phase images, where the number of layers with different resolutions is at least 2, that is, there should be at least two resolution images.

(2) Set the image block size to m=64, use Equation 3 and Equation 4 to divide images of different resolutions into 8×8 image block sets, and convert each image block into 64× A column vector of size 1.

(3) Specify the dimension of the training dictionary as 64×256, select the image block vector set corresponding to the highest resolution image, and solve the sparse coding dictionary D by minimizing Equation 6. Among them, the minimization formula 6 is solved by the following two methods. For the training set encoding algorithm of the sparse encoding dictionary, the variable decomposition and the augmented Lagrangian sparse regression method are used to solve the following problems:

Use encoding to update dictionary elements, as follows:

where d _j is the jth column of dictionary D.

(4) Use sparse coding method to carry out sparse coding on image block vector sets of different resolutions. The algorithm of sparse coding is the algorithm for solving equations 7 and 8. In the implementation of the present invention, a greedy algorithm is used to solve the sparse coding, that is, First select an element from the encoding dictionary, yes, this element can represent the smallest error of the vector to be encoded, and then select an element from the dictionary so that the addition of this element can minimize the representation error, and so on until the encoding error less than the given threshold. In this way, the elements of the dictionary required for encoding and sparse encoding can be obtained.

(5) Calculate the noise reduction result of the image block vector group and the coding dictionary according to the sparse coding, and use Equation 9 and Equation 10 to solve the noise reduction result of each segmented image block.

(6) Use Equation 11 and Equation 12 to calculate the noise reduction results at different resolutions, use the upsampling method to obtain the same size image, and use Equation 15 to calculate the noise reduction results at different resolutions The results are fused.

(7) Use Equation 16 to obtain the phase of the fused image after noise reduction, so as to obtain the noise reduction result of the phase image.

The advantage of the method of the present invention is that compared with the current technology, the present invention proposes a multi-resolution complex number domain adaptive dictionary training algorithm and a sparse coding algorithm for noise reduction estimation, and the method can effectively reduce the noise of the smooth area in the noise reduction image. Pseudo-edge, taking full advantage of the self-similarity of the phase image at multiple resolutions for denoising. The innovation of the present invention is that it proposes a fusion method of multi-resolution noise reduction results. The method of hypothesis testing is used to fuse the noise reduction results of different resolutions. The algorithm can effectively filter out the noise caused by the multi-resolution sampling process. Information loss, and effectively use the multi-resolution noise reduction results.

In general, according to the self-similarity and multi-resolution similarity of the interference phase image, the embodiment of the present invention proposes a multi-resolution sparse algorithm in the complex domain through the realization of the multi-resolution adaptive dictionary training algorithm in the complex domain. The coded phase image noise reduction technology improves the noise reduction effect of complex phases, thereby laying the foundation for phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in magnetic resonance images. In this patent, a two-dimensional wavelet transform method is used to obtain the complex multi-resolution form of the phase image to be denoised, and the obtained multi-resolution images are divided into image blocks to obtain an image block set. Then, the complex coding dictionary is obtained by using the online training method corresponding to the complex image blocks of the original phase image, and the sparse coding coefficients are obtained by encoding the multi-resolution image block set using the dictionary obtained by training. The denoised image block is obtained by multiplying the coding dictionary and the coding coefficients. The image block sets are assembled according to the inverse operation of the segmentation method to obtain the noise reduction results under different resolutions, the noise reduction results of different resolutions are fused to obtain the final complex noise reduction effect, and the complex number is obtained by taking the phase operation to obtain the final phase. Noise reduction results.

Another embodiment of the present invention provides a computer-readable storage medium, where the computer-readable storage medium stores a computer program for signal mapping, and when the computer program is executed by at least one processor, implements any of the foregoing embodiments. A phase information noise reduction algorithm of the multi-resolution sparse coding. The related content can be understood by referring to the method embodiment section, and will not be discussed in detail here.

Although the preferred embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, and therefore, the scope of the present invention should not be limited to the above-described embodiments.

Claims (10)

1. A multi-resolution sparsely encoded phase information noise reduction algorithm, comprising:

acquiring a plurality of multi-resolution images corresponding to the phase image to be denoised, and respectively carrying out image block segmentation on each resolution image to obtain an image block set, wherein the image block set is multiple and is respectively and uniquely corresponding to the resolution images;

respectively executing the following steps to any image block set: obtaining a coding dictionary from the image blocks in the image block set through online training, coding the image block set through the coding dictionary to obtain sparse coding coefficients corresponding to the image block set, multiplying the coding dictionary by the sparse coding coefficients to obtain noise-reduced image blocks, and splicing the image block set according to the inverse operation of segmentation to obtain noise-reduced images;

and fusing the noise-reduced images with different resolutions to obtain a final phase image with a plurality of noise-reduced images, and performing phase operation on the complex number to obtain a final phase noise reduction result.

2. The method according to claim 1, wherein the obtaining of the multi-resolution image corresponding to the complex number of the phase image to be noise-reduced comprises:

passing the phase image to be denoised by z ═ e^jφConverting the image into a corresponding complex resolution image, wherein phi is a phase image to be denoised, e is a natural base number, and j is an imaginary unit;

according to the number of layers of the multi-resolution to be acquired, a two-dimensional Harr wavelet transformation mode is applied to acquire complex images z to be denoised with different resolutions⁽¹⁾,z⁽²⁾,…z^(R)And R is the resolution layer number.

3. The method according to claim 2, wherein the separately performing image block segmentation on each resolution image to obtain an image block set comprises:

the complex image z to be denoised⁽¹⁾,z⁽²⁾,…z^(R)Converting the image blocks into column vectors in a column-by-column splicing mode, segmenting the image blocks of the corresponding vectors of the original image according to the sizes of the segmented image blocks, and defining a selection matrix M_iSo that z is_i＝M_iz, matrix M_iEach row has only one non-zero element and has a value of 1, where z_iIs the ith image block; define the following matrix

wherein ,N_pThe number of image blocks which can be divided by the image z is T, and the T is transposition;

similarly, z for different resolutions⁽¹⁾,z⁽²⁾,…z^(R)Respectively define corresponding partition matrices M⁽¹⁾,M⁽²⁾,…M^(R)By selecting a matrix to segment the original image correspondence vector into sizes

M is an integer squared, i.e.:

4. the method according to claim 3, wherein the obtaining of the coding dictionary by online training of the image blocks of the plurality of phase images to be denoised comprises:

from the collection

In-between randomly acquired image block group z^t,t＝1,…,N_g，N_gPerforming dictionary learning according to the image block groups according to a preset sequence for the number of the image blocks in the selected image block groups, wherein each training cycle adopts one of the image block groups to update dictionary elements, namely performing dictionary training by the following minimization formula:

5. the method according to claim 1, wherein the step of obtaining sparse coding coefficients corresponding to the set of image blocks comprises:

for the image block set under each resolution, carrying out sparse coding on the column vector corresponding to each image block in the image block set, and for the coding dictionary D obtained by training, if the column vector is matched

Each vector z of_iPerforming sparse coding is obtained by solving the following optimization problem

With respect to the resolution r of the image,by solving for

To obtain optimized sparse coding coefficients, where α_iIs z_iIn the encoding of the encoding dictionary D,

is that

Encoding in the encoding dictionary D.

6. The method according to claim 5, wherein said multiplying the coding dictionary by the sparse coding coefficients to obtain the noise-reduced image block comprises:

wherein ,N_rIs the number of image blocks of the r-th resolution,

is z_iThe image block after the noise reduction is performed,

is composed of

And (5) denoising the image block.

7. The method according to claim 5, wherein said stitching the set of image blocks according to an inverse operation of the segmentation to obtain the noise-reduced image comprises:

splicing image block sets under the same resolution according to the following formula to obtain noise-reduced images under different resolutions;

wherein ,

is the result of the noise reduction in z,

is z^(r)The noise reduction result of (1).

8. The method according to claim 5, wherein the fusing the noise-reduced images with different resolutions to obtain a final complex noise reduction effect comprises:

obtaining a final fusion result by using a hypothesis test mode according to the sequence from high resolution to low resolution, wherein the fusion result of each step is used as the fusion input of the next resolution;

firstly, the first step is to

Performing upsampling, obtaining and

same size N₁×N₂Noise reduction result of (2), N₁Is composed of

Length of (2), N₂Is composed of

Is assumed to be as follows:

suppose that

Obeying to the zero mean gaussian distribution, where the standard deviation of the gaussian distribution is σ, and under the condition that the confidence coefficient is 0.95, the following condition should be satisfied for each pixel point in the image

If the above formula is satisfied, when the resolution is assumed to be r 1, the estimation is performed

Is available, otherwise, the estimate may be considered unavailable and will therefore be

And

the fusion result of (A) is

Wherein i is 1,2, …, N₁,j＝1,2,…,N₂；

Similarly, zr is added according to the above method₁And

fusion to give zr₂And obtaining a fusion result zr of the noise reduction result with the resolution R of the last stage_R。

9. The method according to any one of claims 1-8, wherein the phase-extracting the complex number to obtain a final phase noise reduction result comprises:

according to the final fusion result zr of the denoised complex image_RObtaining a complex number zr_RPhase angle of (c) is the final phase estimate:

wherein imag (-) and real (-) compute the real and imaginary parts, respectively.

10. A computer-readable storage medium, characterized in that the computer-readable storage medium stores a signal mapped computer program which, when executed by at least one processor, implements the multi-resolution sparsely encoded phase information noise reduction algorithm of any one of claims 1-9.

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