CN111932473A - Phase information noise reduction algorithm of multi-resolution sparse coding and storage medium - Google Patents
Phase information noise reduction algorithm of multi-resolution sparse coding and storage medium Download PDFInfo
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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
Technical Field
The invention relates to the technical field of complex field interferometry, in particular to a phase information noise reduction algorithm of multi-resolution sparse coding and a computer readable storage medium.
Background
At present, the phase images of a plurality of fields are widely applied to actual measurement, for example, the terrain elevation measurement can be carried out through the interferometric measurement of a synthetic aperture radar, and the global digital elevation data is obtained by the SRTM system of the radar terrain surveying and mapping task of the American space shuttle. It is also possible to measure a change in the terrain or the like due to an earthquake or resource development or the like by interferometry. In the medical field, nuclear magnetic resonance complex images guide diagnosis by complex phase images.
However, whether the synthetic aperture radar interferometry or the nuclear magnetic resonance image measurement is used, due to the existence of factors such as the inherent factors of the measuring equipment and the interference of the measuring environment, noise exists in the final complex measured image, the noise affects the measuring precision, and the subsequent processing can not be performed. Therefore, how to implement denoising becomes a problem which needs to be solved urgently.
Disclosure of Invention
The invention provides a phase information noise reduction algorithm of multi-resolution sparse coding and a computer readable storage medium, which are used for solving the problem that the measurement precision is influenced by the noise in a complex measurement image in the prior art.
In a first aspect, the present invention provides a phase information noise reduction algorithm for multi-resolution sparse coding, including: 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.
Optionally, the acquiring a complex multi-resolution image corresponding to the phase image to be noise-reduced includes:
passing the phase image to be denoised by z ═ ejφConverting 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.
Optionally, respectively performing image block segmentation on the multi-resolution image to obtain an image block set, including:
the complex image z to be denoised(1),z(2),…z(R)Converting the image blocks into column vectors according to a column-by-column splicing mode, firstly segmenting the image blocks of the corresponding vectors of the original image according to the size of the segmented image blocks, and defining a selection matrix MiSo that z isi＝Miz, matrix MiEach row has only one non-zero element and has a value of 1, where ziIs the ith image block; define the following matrix
wherein ,NpThe number of image blocks which can be divided by the image z is T, and the T is transposition;
similarly for z of different resolution(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 generally an integer squared, such as 81, 100, etc., i.e.:
optionally, obtaining an encoding dictionary by performing online training on the phase image to be denoised corresponding to the plurality of image blocks, including:
from the collection
In-between randomly acquired image block group zt,t＝1,…,Ng，NgPerforming 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:
optionally, the step of obtaining an encoding of the set of multi-resolution image blocks comprises:
for an image block set under each resolution, carrying out sparse coding on a column vector corresponding to each image block in the image block set, and for a dictionary D obtained by training, if the column vector is matched
Each vector z ofiPerforming sparse coding is obtained by solving the following optimization problem
For resolution r, by solving
To obtain an optimized encoding. Alpha is alphaiIs ziIn the encoding of the dictionary D,
is that
Encoding in dictionary D.
Optionally, multiplying the coding dictionary by the sparse coding coefficient to obtain a noise-reduced image block, including:
wherein ,NrIs the number of image blocks of the r-th resolution,
is ziThe image block after the noise reduction is performed,
is composed of
And (5) denoising the image block.
Optionally, the splicing the image block set according to an inverse operation of the segmentation to obtain the noise-reduced image with different resolutions includes:
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)Is reduced in noise
Optionally, fusing the noise-reduced images with different resolutions to obtain a final complex noise reduction effect, including:
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 a zero mean gaussian distribution with a standard deviation of σ, then with a confidence of 0.95For each pixel point in the image, the following condition should be satisfied
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 stageR。
Optionally, the obtaining a final phase noise reduction result by performing a complex phase extraction operation includes:
according to the final fusion result zr of the complex imageRObtaining a complex number zrRPhase angle of (c) is the final phase estimate:
In a second aspect, the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a signal-mapped computer program, and when the computer program is executed by at least one processor, the computer program implements the phase information noise reduction algorithm of multi-resolution sparse coding as described in any one of the above.
The invention has the following beneficial effects:
the invention 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, and improves the noise reduction effect of complex phases, thereby laying a foundation for phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in magnetic resonance images.
Drawings
Fig. 1 is a schematic flowchart of a multi-resolution sparsely encoded phase information noise reduction algorithm according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of another multi-resolution sparsely encoded phase information noise reduction algorithm according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a phase information noise reduction algorithm for multi-resolution sparse coding according to an embodiment of the present invention;
fig. 4 is a schematic diagram of sparse coding according to an embodiment of the present invention.
Detailed Description
With the development of signal transformation theory, particularly the discrete fourier transform, discrete cosine transform and discrete wavelet transform, it plays an important role in discrete signal noise reduction in computer systems. The essence of these algorithms is sparse coding, which indicates that natural signals can be represented by a small number of elements in a representation base (also called a dictionary). The basic principle of noise reduction using sparse coding is that a signal space is included in an observation space of a signal, and a dictionary in the sparse coding technology should be a support base of the signal space but not a support base of the signal observation space. In other words, the signal observation space contains signals and noise, the excellent dictionary can well carry out sparse coding on the signals, but can not carry out sparse coding on the noise, and the noise in the observed signals can be effectively filtered through the coding and decoding processes, so that the purposes of removing the noise and improving the precision are achieved. The above analysis can result in that to realize the signal noise reduction problem based on sparse coding, firstly, a good representation dictionary is required, and secondly, effective coding and decoding processes can be carried out. Therefore, the invention focuses on the application and maintenance of the patent in these three aspects.
When sparse coding was originally proposed, the dictionary was fixed, for example by decomposing the signal by a cosine basis in the discrete cosine transform. However, a fixed representation base cannot obtain a high sparsity and cannot obtain a good noise reduction or compression effect. However, the representation dictionary obtained by training the signal to be represented has better adaptivity, so that a more satisfactory representation result can be obtained. Some intelligent algorithms are proposed for training the adaptive dictionary. A redundant representation-based K-SVD algorithm is proposed for image denoising, wherein a representation dictionary is trained by image blocks extracted from a noisy image. Later, the algorithm was extended to the three-dimensional domain to solve the color image repair problem. Some researchers have improved the dictionary training algorithm by stochastic approximation for use in large data of millions of training samples. In 2012, a general approach to supervised dictionary training algorithms was proposed for different classes of tasks. Later dictionaries also start to adapt gradually to group sparse coding, i.e. similar signal blocks should have similar coding based on the same coding dictionary, or codes with the same characteristics.
In order to achieve better encoding of signals and avoid encoding of noise in the encoding and decoding problem, the representation dictionary obtained by training is generally a redundant dictionary, so that the signals are encoded sparsely, that is, a small number of elements in encoding are nonzero, and most elements in the encoding vector are 0. In the actual encoding process, the constraint on the number of zero elements is generally realized by adopting a zero norm regularization mode. However, in the coding optimization problem, the optimization problem obtained by the zero-norm regularization method is non-convex, so that the problem needs to be relaxed into a convex optimization problem or a greedy algorithm needs to be applied to solve to obtain the codes of the observation signals. After the sparse coding is obtained, the original signal can be recovered through the coding dictionary and the sparse coding, and because the coding of noise is avoided in the sparse coding process, the interference of the noise can be filtered after the recovery, and then the noise reduction is realized.
In an algorithm for performing noise reduction on complex-valued phase information by using sparse coding, three important algorithms exist at present: one type is to directly reduce noise of a phase image through a sparse coding technology, the effect obtained by the algorithm is not ideal due to the discontinuity of complex phases and the truncation of the complex phases in an interval [ -pi, pi), and the noise reduction algorithm filters out noise and simultaneously filters out detailed information in partial signals, so that the precision of the signals is reduced. The second type of algorithm is to respectively perform noise reduction on the real part and the imaginary part of the complex value by a sparse coding technology, fuse the noise reduction results of the two parts, obtain the complex value after noise reduction, and obtain the phase of the complex value as the noise reduction result of the phase information in the original complex value. The main disadvantage of the algorithm is that the real part and the imaginary part of the complex number are processed separately, and the correlation between the real part and the imaginary part is ignored, so that the final phase noise reduction result precision value still has a space for improving. The third type of algorithm is to perform noise reduction on the complex value as a whole through a sparse coding technology, the algorithm fully considers the correlation between a real part and an imaginary part in the complex number, and a good noise reduction effect can be obtained through a noise reduction phase obtained by the complex number after noise reduction. The algorithm proposed by the present invention belongs to a third type of noise reduction algorithm. The algorithm of the invention is different from the prior algorithm in that the 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 embodiment of the invention aims to provide a phase image noise reduction technology based on multi-resolution sparse coding in a complex domain by realizing a multi-resolution adaptive dictionary training algorithm in the complex domain according to the self-similarity and multi-resolution similarity of an interference phase image, so that the noise reduction effect of the complex phase is improved, and a foundation is laid for phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in a magnetic resonance image. In the invention, a two-dimensional wavelet transform mode is used to obtain a plurality of multi-resolution forms corresponding to the phase image to be denoised, and the obtained multi-resolution images are respectively subjected to image block division to obtain an image block set. And then, obtaining a complex coding dictionary by using a complex image block corresponding to the original phase image in an online training mode, and coding a multi-resolution image block set by using the dictionary obtained by training to obtain a sparse coding coefficient. And obtaining the image block after noise reduction in a mode of multiplying the coding dictionary by the coding coefficient. And splicing the image block sets according to the inverse operation of the segmentation mode to obtain noise reduction results under different resolutions, fusing the noise reduction results of the different resolutions to obtain a final noise reduction effect of a plurality of numbers, and performing phase operation on the plurality of numbers to obtain a final phase noise reduction result.
In specific implementation, the phase information noise reduction algorithm of multi-resolution sparse coding according to the embodiment of the present invention, as shown in fig. 1, includes:
s101, acquiring a plurality of multi-resolution images corresponding to the phase images to be denoised, and respectively carrying out image block segmentation on each resolution image to obtain an image block set, wherein the image block sets are multiple and respectively and uniquely correspond to the resolution images;
s102, 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;
s103, fusing the noise-reduced images with different resolutions to obtain a final phase image with a complex number after noise reduction, and performing phase operation on the complex number to obtain a final phase noise reduction result.
That is to say, the embodiment of the present invention is a characteristic that, aiming at the problem of noise interference of a phase image, a multi-resolution sparse coding technique is used to code a signal, but random noise cannot be coded. Through the design of the coding and decoding processes and methods, noise in the complex number measuring signals is filtered, the precision of phase information in the complex number measuring signals is improved, and a foundation is laid for later signal application.
The method according to the invention will be explained and illustrated in detail below by means of a specific example in connection with fig. 2 and 3:
in the embodiment of the present invention, the acquiring of the multi-resolution image block set specifically includes:
(a) multi-resolution complex image acquisition:
if the complex number image z corresponding to the phase image is provided for phase noise reduction, the operation is directly performed on the complex number image z, and if the phase image phi containing noise is provided for phase noise reduction, the operation is performed
z＝ejφFormula 1
Converted into a plurality of numbers to perform the following operations.
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)Wherein the low resolution image is only resolved at low frequency after wavelet transform. Since it is obtained by two-dimensional wavelet transform, the length and width of the image of the next level resolution are both half of those of the image of the previous level resolution.
(b) Multi-resolution image block segmentation:
image matrix z, z(1),z(2),…z(R)And converting the column vector into a column vector according to a column-by-column splicing mode. According to the size of the divided image block, firstly, dividing the image block of the corresponding vector of the original image, and defining a selection matrix MiSo that z isi＝Miz (matrix M)iEach row has only one non-zero element and has a value of 1), where ziIs the ith image block. Define the following matrix
wherein ,NpThe number of image blocks that can be divided for the image z. For example, for N ═ N1×N2Image z of size, if it is to be divided into
The number of divided image blocks is
Similarly for z of different resolution(1),z(2),…z(R)Defining a partition matrix M(1),M(2),…M(R). The original image correspondence vector can be divided into sizes by selecting a matrix
Set of image blocks, i.e.
The training of the coding dictionary in the embodiment of the invention specifically comprises the following steps: according to collections
The sparse coding dictionary is obtained through training, the self-adaptive dictionary is obtained through a dictionary training algorithm, the purpose that a coding dictionary needs to be found is to use the linear combination of a small number of dictionary atoms in the coding dictionary to realize the representation of image blocks in a training set, and the training process can be described through the following optimization problem.
wherein 
Wherein the former term is a representation error and the latter term is a sparse constraint term, both terms being balanced by a regularization parameter λ > 0. The constraint D e C is to prevent 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 practical experiments, the encoding dictionary obtained by the L1 norm method has better effect on the complex noise reduction.
The general approach to solving problem 5 is to interactively encode dictionary D
And respectively carrying out optimization solution. The solution to the D optimization is a quadratic optimization problem on a convex set, and
the optimization is a convex optimization problem and resolvable. Optimization problem equation 5 the optimization problem for dictionary D is relatively simple, but for encoding
The optimization solution is very time consuming. In order to improve the calculation efficiency and reduce the problem of solving the dictionary training, the invention adopts an online dictionary training method. First from the set
In-between randomly acquired image block group zt,t＝1,…,NgThen, dictionary learning is performed according to the image block groups in a certain order. And each cycle of training adopts one image block group to update dictionary elements. I.e. dictionary training by minimizing the following.
The encoding for acquiring the multi-resolution image block set in the embodiment of the present invention specifically includes:
for the image block set at each resolution, the column vector corresponding to each image block in the image block set is sparsely encoded, as shown in fig. 4. For the dictionary D obtained by training, if pair
Each vector z ofiPerforming 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 optimization problem can be solved using a greedy algorithm.
The fusion of the multi-resolution image blocks in the embodiment of the invention specifically comprises the following steps:
(a) acquiring a multi-resolution complex image denoising image block:
through the above steps, we have obtained the sparse coding dictionary D and the codes at the respective resolutions, and can obtain the noise reduction result of the segmented image block by multiplying the coding dictionary by the sparse coding.
Namely, it is
(b) Splicing of image block sets:
after the denoising set of the image blocks is obtained, the inverse operation of image block segmentation is carried out aiming at a plurality of resolutions, and the image blocks under the same resolution are combined to synthesize the whole image. The splicing process is the inverse operation of equation 3 and equation 4.
Through the operation, the noise reduction estimation result of the complex number corresponding to the original phase image is obtained
And a noise reduction estimation result corresponding to the resolution r
How will the following steps of the invention
And noise reduction results of different resolutions
And (5) carrying out fusion to obtain a final noise reduction result. This is part of the major maintenance of the invention.
(c) And (3) fusing multi-resolution noise reduction results:
in the fusion process of the noise reduction results with different resolutions, the method adopts a high-resolution to low-resolution mode and a hypothesis testing mode to obtain the final fusion result. The fusion result of each step is used as the fusion input of the next resolution.
First of all see
And
firstly, the first step is to
Performing upsampling, obtaining and
same size N1×N2The noise reduction result of (1). The following is assumed:
can assume 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 equation 14 is satisfied, it can be assumed that when the resolution is 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. In the same manner as described below for zr1In that
Fusion to give zr2So as to continue to obtain the fusion result zr of the noise reduction result with the resolution R of the last stageR。
(d) Obtaining a phase image noise reduction result:
according to the final fusion result zr of the complex imageRObtaining a complex number zrRIs the final phase estimate.
Wherein imag (-) and real (-) compute the real and imaginary parts, respectively.
The main point of the method is to use a hypothesis testing method to fuse the multi-resolution noise reduction results, namely, the calculation mode of formula 15. Before the fusion of the denoising results, multi-resolution decomposition is carried out by using wavelet transformation, the sparse coding dictionary is trained by using formula 6 for resolution, sparse coding is carried out by using formula 7 and formula 8, and finally the denoising blocks are combined by the inverse operation of blocking to obtain the denoising results under different resolutions.
The method mainly comprises the following steps:
(1) converting the input phase image into a complex form, taking the complex amplitude as the amplitude if the amplitude is known, and setting the amplitude as 1 if the amplitude is not input, and acquiring phase images with different resolutions by applying a wavelet change mode to the phase image, wherein the number of layers of the different resolutions is at least 2, namely, the phase image at least should have two resolutions.
(2) Setting the image block size to m-64, dividing an image of different resolutions into a set of 8 × 8 sized image blocks using equations 3 and 4, and converting each image block into a 64 × 1 sized column vector in a column-stacked manner.
(3) And (3) specifying the dimensionality of the training dictionary to be 64 multiplied by 256, selecting an image block vector set corresponding to the image with the highest resolution, and solving the sparse coding dictionary D by applying a minimization formula 6. The minimum formula 6 is solved by adopting the following two methods, and the following problems are solved by adopting a variable decomposition and augmented Lagrange sparse regression method for a training set coding algorithm of a sparse coding dictionary:
updating dictionary elements by using coding, which comprises the following steps:
wherein djColumn j of the dictionary D.
(4) The sparse coding method is used for carrying out sparse coding on image block vector sets with different resolutions, the sparse coding algorithm is an algorithm for solving equations 7 and 8, a greedy algorithm is adopted for solving the sparse coding in the implementation of the sparse coding method, namely, an element is selected from a coding dictionary and can represent the minimum error of a vector to be coded, and then an element is selected from the dictionary, so that the addition of the element can reduce the representation error to the maximum extent, and the process is circulated until the coding error is smaller than a given threshold value. Thus, the elements of the dictionary required for encoding and sparse encoding can be obtained.
(5) And calculating a noise reduction result of the image block vector group and a coding dictionary according to sparse coding, and solving the noise reduction result of each divided image block by using an equation 9 and an equation 10.
(6) And calculating to obtain noise reduction results under different resolutions by using the equations 11 and 12, obtaining images with the same size by applying the noise reduction results under different resolutions in an upsampling mode, and fusing the noise reduction results under different resolutions by using the equation 15.
(7) And (3) acquiring the phase of the fused image after noise reduction by using the formula 16, thereby acquiring the noise reduction result of the phase image.
Compared with the prior art, the method has the advantages that the multi-resolution complex number field self-adaptive dictionary training algorithm and the sparse coding algorithm are provided for noise reduction estimation, the false edge of a smooth area in a noise reduction image can be effectively reduced, and the self-similarity of a phase image under the multi-resolution is fully utilized for noise reduction. The innovation of the invention is to provide a fusion method of multi-resolution noise reduction results, which fuses the noise reduction results with different resolutions by using a hypothesis test method.
Generally speaking, the embodiment of the invention provides a phase image noise reduction technology based on multi-resolution sparse coding in a complex domain by realizing a multi-resolution adaptive dictionary training algorithm in the complex domain according to the self-similarity and multi-resolution similarity of an interference phase image, and improves the noise reduction effect of the complex phase, thereby laying a foundation for phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in a magnetic resonance image. In the patent, a two-dimensional wavelet transform mode is used to obtain a multi-resolution form of a corresponding complex number of a phase image to be denoised, and the obtained multi-resolution image is subjected to image block segmentation to obtain an image block set. And then, obtaining a complex coding dictionary by using a complex image block corresponding to the original phase image in an online training mode, and coding a multi-resolution image block set by using the dictionary obtained by training to obtain a sparse coding coefficient. And obtaining the image block after noise reduction in a mode of multiplying the coding dictionary by the coding coefficient. And splicing the image block sets according to the inverse operation of the segmentation mode to obtain noise reduction results under different resolutions, fusing the noise reduction results of the different resolutions to obtain a final noise reduction effect of a plurality of numbers, and performing phase operation on the plurality of numbers to obtain a final phase noise reduction result.
Another embodiment of the present invention provides a computer-readable storage medium storing 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 the above embodiments. Relevant matters can be understood by referring to the part of the embodiment of the method, and are not 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 the scope of the invention should not be limited to the embodiments described above.
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 ═ ejφConverting 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 MiSo that z isi＝Miz, matrix MiEach row has only one non-zero element and has a value of 1, where ziIs the ith image block; define the following matrix
wherein ,NpThe 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 zt,t＝1,…,Ng，NgPerforming 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 ofiPerforming 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 αiIs ziIn 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 ,NrIs the number of image blocks of the r-th resolution,
is ziThe 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 stageR。
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 imageRObtaining a complex number zrRPhase angle of (c) is the final phase estimate:
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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