CN111932473B - Multi-resolution sparse coding phase information noise reduction algorithm and storage medium - Google Patents
Multi-resolution sparse coding phase information noise reduction algorithm and storage medium Download PDFInfo
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Abstract
The invention discloses a phase information noise reduction algorithm and a storage medium of multi-resolution sparse coding, which are used for providing a phase image noise reduction technology based on multi-resolution sparse coding in a complex domain according to the self-similarity and multi-resolution similarity of interference phase images and through the realization of a multi-resolution self-adaptive dictionary training algorithm in the complex domain, improving 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.
Description
Technical Field
The invention relates to the technical field of complex domain 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 image of the complex domain is widely applied to actual measurement, for example, the measurement of the topography elevation can be carried out through interferometry of a synthetic aperture radar, and the global digital elevation data is acquired by using the measurement method by an SRTM system of the topography mapping task of the American spaceflight radar. Changes in terrain due to earthquakes, resource development, or the like can also be measured by interferometry. In the medical field, nuclear magnetic resonance complex images guide diagnosis through complex phase images.
However, whether the synthetic aperture radar interferometry or the nuclear magnetic resonance image measurement is used, noise exists in the final complex measurement image due to factors such as inherent factors of the measurement equipment and interference of the measurement environment, and the noise affects the measurement accuracy and may cause subsequent processing to be impossible. How to implement denoising is a problem that needs to be solved.
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 accuracy is affected by 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, the method comprising: acquiring a plurality of multi-resolution images corresponding to a phase image to be noise reduced, and respectively carrying out image block segmentation on each resolution image to obtain image block sets, wherein the number of the image block sets is multiple, and the image block sets are respectively and uniquely corresponding to the resolution images; the following steps are respectively executed for any image block set: the method comprises the steps of obtaining an image block in the image block set through online training, encoding the image block set through the encoding dictionary to obtain sparse encoding coefficients corresponding to the image block set, multiplying the encoding dictionary by the sparse encoding coefficients to obtain a noise-reduced image block, and splicing the image block set according to the split inverse operation to obtain a noise-reduced image; and fusing the noise-reduced images with different resolutions to obtain a final complex noise-reduced phase image, and performing phase extraction operation on the complex to obtain a final phase noise reduction result.
Optionally, the acquiring a multi-resolution image of the complex number corresponding to the phase image to be noise reduced includes:
passing the phase image to be noise reduced through z=e jφ Converting the image into a resolution image corresponding to a complex number, wherein phi is a phase image to be noise reduced, e is a natural base number, and j is an imaginary unit;
according to the number of layers of the multi-resolution needed to be acquired, the method usesTwo-dimensional Harr wavelet transformation mode for obtaining complex images z with different resolutions to be noise reduced (1) ,z (2) ,…z (R) R is the number of resolution layers.
Optionally, the image block segmentation is performed on the multi-resolution image to obtain an image block set, which includes:
the complex image z to be noise reduced (1) ,z (2) ,…z (R) Converting the image block into column vectors in a column-by-column splicing mode, firstly dividing the image block by the vector corresponding to the original image according to the size of the divided image block, and defining a selection matrix M i So that z i ＝M i z, matrix M i Each row has only one non-zero element and has a value of 1, where z i Is the ith image block; defining the following matrix wherein ,Np The number of image blocks which can be divided for the image z is T, and the T is the transposition;
z for different resolutions (1) ,z (2) ,…z (R) Respectively define the corresponding dividing matrix M (1) ,M (2) ,…M (R) Dividing the original image corresponding vector into the size by selecting matrixM is generally an integer squared, e.g. 81, 100, etc., i.e.:
optionally, the obtaining the coding dictionary by on-line training of the image block of the complex number corresponding to the phase image to be noise reduced includes:
from a collectionRandom acquisition of image block group z t ,t＝1,…,N g ，N g For the number of image blocks in the selected image block group, dictionary learning is performed according to the image block groups according to a predetermined sequence, and each cycle of training adopts one of the image block groups to update dictionary elements, namely dictionary training is performed by minimizing the following formula:
optionally, the step of obtaining the encoding of the set of multi-resolution image blocks comprises:
for each image block set under each resolution, sparse coding is carried out on column vectors corresponding to each image block in the image block set, and for the dictionary D obtained by training, ifEach of the vectors z i Sparse coding is obtained by solving the following optimization problem
For resolution r, by solving forTo obtain an optimized code. Alpha i Is z i Coding in dictionary D, < >>Is->Coding on dictionary D.
Optionally, multiplying the coding dictionary with the sparse coding coefficient to obtain a denoised image block, including:
wherein ,Nr The number of image blocks for the r-th resolution,is z i Noise-reduced image block->Is->And denoising the image block.
Optionally, stitching the image block set according to the inverse operation of segmentation to obtain the image after noise reduction under different resolutions, including:
splicing the image block sets under the same resolution according to the following formula to obtain images after noise reduction under different resolutions;
wherein ,is the noise reduction result of z>Is z (r) Noise reduction results of (a)
Optionally, fusing the denoised images with different resolutions to obtain a final complex denoising 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;
will firstUpsampling to obtain AND ∈ ->The same size N 1 ×N 2 N, is the noise reduction result of (2) 1 Is->Length of N 2 Is->Is assumed as follows:
assume thatFollowing a zero-mean gaussian distribution, the standard deviation of which is σ, then for each pixel in the image, with a confidence level of 0.95, the following condition should be satisfied
If the above expression is satisfied, it is estimated that the resolution is r=1Is available, otherwise, it can be considered that the estimation is not availableUse, therefore will-> and />The fusion result of (2) is
Where i=1, 2, …, N 1 ,j＝1,2,…,N 2 ；
Similarly, zr is determined as described above 1 And (3) withFusion is carried out to obtain zr 2 And obtaining a fusion result zr of the noise reduction result of the final level resolution R R 。
Optionally, the step of performing the complex phase extraction operation to obtain a final phase noise reduction result includes:
based on the fusion result zr of the final complex image R Obtaining complex zr R Is the most final phase estimate:
wherein imag (·) and real (·) are calculated real and imaginary parts, respectively.
In a second aspect, the present invention provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program for signal mapping, which when executed by at least one processor, implements a multi-resolution sparse coded phase information noise reduction algorithm as described in any one of the above.
The invention has the following beneficial effects:
according to the self-similarity and multi-resolution similarity of interference phase images, the invention provides a multi-resolution sparse coding-based phase image noise reduction technology in a complex domain through the realization of a multi-resolution self-adaptive dictionary training algorithm in the complex domain, 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 flow chart of a phase information noise reduction algorithm of multi-resolution sparse coding according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of another phase information noise reduction algorithm of multi-resolution sparse coding 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, in particular, the proposals of discrete fourier transformation, discrete cosine transformation and discrete wavelet transformation, the signal transformation theory plays a great role in the noise reduction of discrete signals in a computer system. The essence of these algorithms is sparse coding, which suggests that natural signals can be represented by a small number of elements in a representation base (also called dictionary). The basic principle of noise reduction by using sparse coding is that a signal space is contained 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 cannot carry out sparse coding on the noise, and through the coding and decoding processes, the noise in the observation signals can be effectively filtered, so that the purposes of removing the noise and improving the precision are achieved. The above analysis can obtain that to realize the signal noise reduction problem based on sparse coding, it is necessary to have an excellent representation dictionary first and then to perform an efficient encoding and decoding process second. The present invention is therefore focused on the application and maintenance of these three aspects.
When sparse coding was originally proposed, the dictionary was fixed, for example by cosine-base decomposing the signal in discrete cosine transform. However, the fixed representation base does not achieve high sparsity and does not achieve good noise reduction or compression. However, the representation dictionary obtained through training of the signals to be represented has better adaptivity, so that more satisfactory representation results can be obtained. Some intelligent algorithms have been proposed for training adaptive dictionaries. A K-SVD algorithm based on redundant representation is proposed for use in image denoising, wherein the representation dictionary is trained from image blocks extracted from noisy images. Later, the algorithm was extended to the three-dimensional domain to solve the problem of color image restoration. Some researchers have improved dictionary training algorithms by stochastic approximation for use in large data of millions of training samples. In 2012, a general approach to a supervised dictionary training algorithm was proposed for use in different classes of tasks. Later dictionaries also begin to adapt gradually to the group sparse coding, i.e. similar signal blocks should have similar coding based on the same coding dictionary, or the coding should have the same characteristics.
In terms of coding and decoding, in order to achieve that the coding algorithm can better code the signal and avoid coding noise, the representation dictionary obtained by general training is a redundant dictionary, so that the coding of the signal is sparse, i.e. a small number of elements in the coding are non-zero, and most of elements in the coding vector are 0. In the actual encoding process, a zero norm regularization mode is generally adopted to realize the constraint on the number of zero elements. However, in the coding optimization problem, the optimization problem obtained by adopting 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 is used for solving to obtain the coding of the observation signal. After the sparse coding is obtained, the original signal can be restored through the coding dictionary and the sparse coding, and noise is prevented from being coded in the sparse coding process, so that noise interference can be filtered after the sparse coding is restored, and noise reduction is further achieved.
Among algorithms for performing noise reduction on complex-valued phase information by using sparse coding, three important algorithms exist at present: the noise reduction is directly carried out on the phase image through a sparse coding technology, the discontinuity of the complex phases is cut off in a range of [ -pi, pi), the effect obtained by the algorithm is not ideal, the noise reduction algorithm filters detail information in part of signals while filtering noise, and the accuracy of the signals is reduced. The second type of algorithm is to respectively denoise the real part and the imaginary part of the complex value through a sparse coding technology, and to fuse the denoise results of the two parts to obtain a denoised complex value, and to obtain a complex value phase as a denoise result of 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 independently, the association relation between the real part and the imaginary part is ignored, and the final phase noise reduction result precision value still has a space for improvement. The third type of algorithm is to make noise reduction on complex values as a whole through a sparse coding technology, the algorithm fully considers the correlation between the real part and the imaginary part in the complex, and the noise reduction phase obtained by the complex after noise reduction can obtain a good noise reduction effect. The algorithm proposed by the present invention belongs to the third type of noise reduction algorithm. The algorithm is different from the previous algorithm in that the noise reduction is realized by the multi-resolution dictionary training and sparse coding mode, so that the noise reduction effect of the phase image is further improved.
The embodiment of the invention aims to provide a phase image noise reduction technology based on multi-resolution sparse coding in a complex domain according to the self-similarity and multi-resolution similarity of interference phase images, and provides a phase image noise reduction technology based on multi-resolution sparse coding in the complex domain, so that the noise reduction effect of complex phases is improved, and the foundation is laid for phase noise reduction in synthetic aperture radar interferometry and phase noise reduction in magnetic resonance images. In the invention, a two-dimensional wavelet transformation mode is used for obtaining a multi-resolution form of a complex number corresponding to a phase image to be reduced, and the obtained multi-resolution image is respectively subjected to image block segmentation to obtain an image block set. And then, a complex coding dictionary is obtained by an online training mode through the complex image blocks corresponding to the original phase image, and a multi-resolution image block set is coded by using the dictionary obtained by training to obtain sparse coding coefficients. And obtaining the image block after noise reduction by multiplying the coding dictionary and 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 with different resolutions to obtain a final complex noise reduction effect, and performing complex phase extraction operation 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, referring to fig. 1, includes:
s101, acquiring a plurality of multi-resolution images corresponding to a phase image to be noise reduced, and respectively carrying out image block segmentation on each resolution image to obtain image block sets, wherein the number of the image block sets is multiple, and the image block sets are respectively and uniquely corresponding to the resolution images;
s102, executing the following steps on any image block set: the method comprises the steps of obtaining an image block in the image block set through online training, encoding the image block set through the encoding dictionary to obtain sparse encoding coefficients corresponding to the image block set, multiplying the encoding dictionary by the sparse encoding coefficients to obtain a noise-reduced image block, and splicing the image block set according to the split inverse operation to obtain a noise-reduced image;
s103, fusing the noise-reduced images with different resolutions to obtain a final complex noise-reduced phase image, and performing complex phase extraction operation to obtain a final phase noise reduction result.
That is, the embodiment of the invention is characterized in that the signal is encoded by using a multi-resolution sparse coding technology aiming at the noise interference problem of the phase image, but random noise cannot be encoded. Noise in the complex measurement signals is filtered through the design of the coding and decoding processes and methods, so that the accuracy of phase information in the complex measurement 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 way of a specific example in connection with fig. 2 and 3:
in the embodiment of the present invention, the acquiring 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, the complex image z is directly operated, and if the noise-containing phase image phi is provided for phase noise reduction, the complex image z is operated by
z＝e jφ 1 (1)
The conversion to plural numbers proceeds the following operations.
According to the number of layers of multiple resolutions to be acquired, acquiring complex images z with different resolutions to be noise reduced by using a two-dimensional Harr wavelet transformation mode (1) ,z (2) ,…z (R) Wherein the low resolution image only takes the low frequency resolution after wavelet transformation. Since acquired by two-dimensional wavelet transform, the length and width of the lower-level resolution image are half of those of the upper-level resolution image.
(b) Multi-resolution image block segmentation:
matrix z, z of images (1) ,z (2) ,…z (R) And converting the data into column vectors in a column-by-column splicing mode. According to the size of the segmented image block, firstly, the corresponding vector of the original image is segmented into the image blocks, and a selection matrix M is defined i So that z i ＝M i z (matrix M i Each row has only one non-zero element and has a value of 1), where z i Is the i-th image block. Defining the following matrix
wherein ,Np The number of image blocks that can be divided for the image z. For N=N, for example 1 ×N 2 An image z of size, if it is to be divided intoThe number of divisions is +.>
Z for different resolutions (1) ,z (2) ,…z (R) Defining a segmentation matrix M (1) ,M (2) ,…M (R) . The original image corresponding vector can be divided into the size by selecting a matrixOf image blocks, i.e.
The training of the coding dictionary in the embodiment of the invention specifically comprises the following steps: according to the collectionThe sparse coding dictionary is obtained through training, the purpose of obtaining the self-adaptive dictionary through a dictionary training algorithm is to find a coding dictionary, the representation of the image blocks in the training set can be realized through the linear combination of a small number of dictionary atoms in the coding dictionary, and the training process can be described through the following optimization problem.
wherein Where the former term represents the error and the latter term represents the sparsity constraint term, the two terms being balanced by a regularization parameter λ > 0. The constraint D ε C is to prevent elements in the dictionary from tending to be arbitrarily large. In equation (5), the latter sparsity constraint is constrained by the L1 norm, because in practical experiments, the L1 norm-wise derived dictionary has better effect on complex noise reduction。
The general approach to solve problem 5 is to interactively encode the dictionary DAnd respectively carrying out optimization solution. Solving the D-optimization is a quadratic optimization problem on a convex set, for +.>Optimization is a convex optimization problem and is decomposable. Optimization problem equation 5 is relatively simple for the dictionary D optimization problem, but +_for coding>The optimization solution is very time consuming. In order to improve the calculation efficiency and reduce the dictionary training, the invention adopts an online dictionary training method. First from the collection->Random acquisition of image block group z t ,t＝1,…,N g Dictionary learning is then performed in a certain order from these image block groups. Each cycle of training uses one of the image block sets for dictionary element updating. I.e., dictionary training, by minimizing the following equation.
The method for obtaining the multi-resolution image block set in the embodiment of the invention specifically comprises the following steps:
for each image block set under each resolution, sparse coding is performed on column vectors corresponding to each image block in the image block set, as shown in fig. 4. For the dictionary D obtained by training, if toEach of the vectors z i Sparse coding is obtained by solving the following optimization problemObtaining the product
For the resolution r, it can be obtained by solving the following optimization problem.
The optimization problem described above may 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) Obtaining a multi-resolution complex image noise reduction image block:
through the above steps, we have acquired the sparse coding dictionary D and the codes at the respective resolutions, and the noise reduction result of the divided image blocks can be acquired by multiplying the coding dictionary by the sparse coding.
I.e.
(b) Stitching of image block sets:
after the noise reduction set of the image blocks is obtained, the inverse operation of image block segmentation is carried out for a plurality of resolutions, and the image blocks with the same resolution are combined to form a whole image. The split process is the inverse operation of formulas 3 and 4.
Through the operation, the complex noise reduction estimation result corresponding to the original phase image is obtainedAnd a noise reduction estimation result +.>How +.>And noise reduction results of different resolutions +.>And (5) fusing to obtain a final noise reduction result. This is the part of the invention that is of major maintenance.
(c) Fusion of multi-resolution noise reduction results:
in the fusion process of the noise reduction results with different resolutions, the invention adopts a hypothesis test mode from a high resolution mode to a low resolution mode to obtain a final fusion result. The fusion result of each step is used as the fusion input of the next resolution.
First look at and />First will->Upsampling to obtain AND ∈ ->The same size N 1 ×N 2 Is a noise reduction result of (1). The following is assumed:
it can be assumed thatFollowing a zero-mean gaussian distribution, the standard deviation of which is σ, then for each pixel in the image, with a confidence level of 0.95, the following condition should be satisfied
If equation 14 is satisfied, it can be considered that the resolution is r=1, and the estimation is performedIs available, otherwise, the estimate can be considered unavailable, so will +.> and />The fusion result of (2) is
Where i=1, 2, …, N 1 ,j＝1,2,…,N 2 . The same procedure is used to apply zr as follows 1 In the followingFusion is carried out to obtain zr 2 Thus, the fusion result zr of the noise reduction result of the final level resolution R is obtained R 。
(d) Obtaining a phase image noise reduction result:
based on the fusion result zr of the final complex image R Obtaining complex zr R Is the most estimated value of the final phase.
Wherein imag (·) and real (·) are calculated real and imaginary parts, respectively.
The main key point of the method is to use a hypothesis testing method to fuse the multi-resolution noise reduction results, namely the calculation mode of the formula 15. Before the fusion of the noise reduction results, the wavelet transformation is used for carrying out multi-resolution decomposition, the equation 6 is used for carrying out sparse coding dictionary training, the equation 7 and the equation 8 are used for carrying out sparse coding, and finally the blocks after noise reduction are combined through the inverse operation of the blocks, so that the noise reduction results under different resolutions are obtained.
The method mainly comprises the following steps:
(1) The input phase image is converted into a complex form, if the amplitude is known, the complex amplitude is used as the complex amplitude, if the amplitude is not input, the amplitude is set to be 1, the phase image is obtained by using a wavelet change mode, and the phase images with different resolutions have at least 2 layers, namely the images with at least two resolutions.
(2) The image block size is set to m=64, the images of different resolutions are divided into 8×8-sized image block sets using equations 3 and 4, and each image block is converted into a 64×1-sized column vector in a column stack manner.
(3) The dimension of the designated training dictionary is 64×256, the image block vector set corresponding to the highest resolution image is selected, and the sparse coding dictionary D is solved by using the method of minimizing equation 6. The minimization type 6 is solved by adopting the following two methods, and the following problems are solved by adopting a variable decomposition and augmentation Lagrangian sparse regression method for a training set coding algorithm of the sparse coding dictionary:
the dictionary elements are updated by using codes, and the method is concretely as follows:
wherein dj Is the j-th column of dictionary D.
(4) The method comprises the steps of performing sparse coding on image block vector sets with different resolutions by using a sparse coding method, wherein the algorithm of the sparse coding is an algorithm of a solution formula 7 and an algorithm of a solution formula 8, and in the execution of the method, a greedy algorithm is adopted to perform the solution of the sparse coding, namely, firstly, one element is selected from a coding dictionary, the element can represent the vector to be coded with the minimum error, and then, one element is selected from the dictionary, so that the addition of the element can reduce the representation error to the maximum extent, and the method is circulated until the coding error is smaller than a given threshold value. Thus, elements of the dictionary required for encoding and sparse encoding can be obtained.
(5) And (3) 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 the formulas 9 and 10.
(6) The noise reduction results under different resolutions are calculated by using the formulas 11 and 12, the same-size image is obtained by using an up-sampling mode on the noise reduction results under different resolutions, and the noise reduction results under different resolutions are fused by using the formula 15.
(7) And 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 method provided by the invention carries out noise reduction estimation by the multi-resolution complex domain self-adaptive dictionary training algorithm and the sparse coding algorithm, can effectively reduce the pseudo edges of the smooth area in the noise reduction image, and fully utilizes the self-similarity of the phase image under the multi-resolution to carry out noise reduction. The invention has the innovation that a multi-resolution noise reduction result fusion method is provided, the noise reduction results with different resolutions are fused by using a hypothesis test method, and the algorithm can effectively filter out information loss in the multi-resolution sampling process and effectively utilize the multi-resolution noise reduction results.
In general, according to the self-similarity and multi-resolution similarity of the interference phase images, the embodiment of the invention provides a multi-resolution sparse coding-based phase image noise reduction technology in a complex domain through the realization of a multi-resolution self-adaptive dictionary training algorithm in the complex domain, and improves the noise reduction effect of complex phases, thereby laying a foundation for realizing phase noise reduction in the interferometry of the synthetic aperture radar and phase noise reduction in the magnetic resonance image. In the patent, a two-dimensional wavelet transformation mode is used for obtaining a multi-resolution form of a complex number corresponding to a phase image to be reduced, and the obtained multi-resolution images are respectively subjected to image block segmentation to obtain an image block set. And then, a complex coding dictionary is obtained by an online training mode through the complex image blocks corresponding to the original phase image, and a multi-resolution image block set is coded by using the dictionary obtained by training to obtain sparse coding coefficients. And obtaining the image block after noise reduction by multiplying the coding dictionary and 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 with different resolutions to obtain a final complex noise reduction effect, and performing complex phase extraction operation to obtain a final phase noise reduction result.
Another embodiment of the present invention provides a computer-readable storage medium storing a computer program of signal mapping, which when executed by at least one processor, implements the multi-resolution sparse coded phase information noise reduction algorithm of any of the above embodiments. The relevant content may be understood with reference to the method embodiments section and will not be discussed in detail herein.
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 accordingly the scope of the invention is not limited to the embodiments described above.
Claims (8)
1. A method for noise reduction of phase information for multi-resolution sparse coding, comprising:
acquiring a plurality of multi-resolution images corresponding to a phase image to be noise reduced, and respectively carrying out image block segmentation on each resolution image to obtain image block sets, wherein the number of the image block sets is multiple, and the image block sets are respectively and uniquely corresponding to the resolution images;
the following steps are respectively executed for any image block set: the method comprises the steps of obtaining an image block in the image block set through online training, encoding the image block set through the encoding dictionary to obtain sparse encoding coefficients corresponding to the image block set, multiplying the encoding dictionary by the sparse encoding coefficients to obtain a noise-reduced image block, and splicing the image block set according to the split inverse operation to obtain a noise-reduced image;
fusing the noise-reduced images with different resolutions to obtain a final complex noise-reduced phase image, and performing phase extraction operation on the complex to obtain a final phase noise reduction result;
the step of obtaining sparse coding coefficients corresponding to the set of image blocks comprises: for each image block set under each resolution, sparse coding is carried out on column vectors corresponding to each image block in the image block set, and for the coding dictionary D obtained by training, ifEach of the vectors z i Sparse coding is obtained by solving the following optimization problem
For resolution r, by solving forTo obtain an optimized sparse coding coefficient, wherein α i Is z i Coding in coding dictionary D, ++>Is->Encoding on the encoding dictionary D;
multiplying the coding dictionary by the sparse coding coefficient to obtain a denoised image block, wherein the method comprises the following steps of:
wherein ,Nr The number of image blocks for the r-th resolution,is z i Noise-reduced image block->Is->And denoising the image block.
2. The method of claim 1, wherein the acquiring a multi-resolution image of a complex number corresponding to the phase image to be denoised comprises:
passing the phase image to be noise reduced through z=e jφ Converting the image into a resolution image corresponding to a complex number, wherein phi is a phase image to be noise reduced, e is a natural base number, and j is an imaginary unit;
according to the number of layers of multi-resolution to be acquired, a two-dimensional Harr wavelet transform method is appliedAcquiring complex images z with different resolutions to be noise reduced (1) ,z (2) ,…z (R) R is the number of resolution layers.
3. The method according to claim 2, wherein the performing image block segmentation on each resolution image to obtain the image block set includes:
the complex image z to be noise reduced (1) ,z (2) ,…z (R) Converting the image block into column vectors in a column-by-column splicing mode, dividing the image block by the vector corresponding to the original image according to the size of the divided image block, and defining a selection matrix M i So that z i ＝M i z, matrix M i Each row has only one non-zero element and has a value of 1, where z i Is the ith image block; defining the following matrix wherein ,Np The number of image blocks which can be divided for the image z is T, and the T is the transposition;
similarly, for z of different resolutions (1) ,z (2) ,…z (R) Respectively define the corresponding dividing matrix M (1) ,M (2) ,…M (R) Dividing the original image corresponding vector into the size by selecting matrixM is the square of the integer, i.e.:
4. a method according to claim 3, wherein obtaining the coding dictionary by on-line training the image blocks of the plurality of corresponding to the phase image to be denoised comprises:
from a collectionRandom acquisition of image block group z t ,t＝1,…,N g ，N g For the number of image blocks in the selected image block group, dictionary learning is performed according to the image block groups according to a predetermined sequence, and each cycle of training adopts one of the image block groups to update dictionary elements, namely dictionary training is performed by minimizing the following formula:
5. the method according to claim 1, wherein the stitching the image block set according to the inverse of the segmentation to obtain the noise-reduced image includes:
splicing the image block sets under the same resolution according to the following formula to obtain images after noise reduction under different resolutions;
wherein ,is the noise reduction result of z>Is z (r) Is a noise reduction result of (a).
6. The method according to claim 1, wherein the fusing the denoised images of different resolutions to obtain a final complex denoising effect includes:
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;
will firstUpsampling to obtain AND ∈ ->The same size N 1 ×N 2 N, is the noise reduction result of (2) 1 Is->Length of N 2 Is->Is assumed as follows:
H 0 :
H 1 :
assume thatFollowing a zero-mean gaussian distribution, the standard deviation of which is σ, then for each pixel in the image, with a confidence level of 0.95, the following condition should be satisfied
If the above expression is satisfied, it is estimated that the resolution is r=1Is available, otherwise, the estimate can be considered unavailable, so will +.> and />The fusion result of (2) is
Where i=1, 2, …, N 1 ,j＝1,2,…,N 2 ；
Similarly, zr is determined as described above 1 And (3) withFusion is carried out to obtain zr 2 And obtaining a fusion result zr of the noise reduction result of the final level resolution R R 。
7. The method according to any one of claims 1-6, wherein said subjecting the complex phase-taking operation to a final phase noise reduction result comprises:
according to the fusion result zr of the complex image after final noise reduction R Obtaining complex zr R Is the most final phase estimate:
wherein imag (·) and real (·) are calculated real and imaginary parts, respectively.
8. A computer readable storage medium, characterized in that the computer readable storage medium stores a computer program of signal mapping, which computer program, when being executed by at least one processor, implements the multi-resolution sparse coded phase information noise reduction method of any one of claims 1-7.
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