CN107492129B - Non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering - Google Patents

Non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering Download PDF

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CN107492129B
CN107492129B CN201710707916.4A CN201710707916A CN107492129B CN 107492129 B CN107492129 B CN 107492129B CN 201710707916 A CN201710707916 A CN 201710707916A CN 107492129 B CN107492129 B CN 107492129B
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刘芳
李婉
李婷婷
陈璞花
郝红侠
焦李成
马文萍
古晶
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Abstract

The invention discloses a non-convex compressed sensing optimization reconstruction method based on sketch representation and structured clustering, which mainly solves the problem of inaccurate reconstruction of compressed sensing images under low sampling rate, and the realization process is as follows: defining a sketch block and a non-sketch block according to a sketch of an image, wherein the non-sketch block comprises an optical sliding block and a texture block, and the sketch block comprises a unidirectional block and a multidirectional block; the unidirectional blocks adopt clustering based on sketch direction guidance; clustering based on direction distribution characteristics is adopted for the multi-directional blocks; the light sliding block and the texture block adopt gray level clustering; carrying out multi-measurement vector observation on each type of image block; during reconstruction, a final reconstructed image is obtained by adopting a particle swarm algorithm based on intersection and atom direction constraint according to the multi-measurement matrix, the category index and the direction information of each type of image block.

Description

Non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to a non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering, which can be used for reconstructing natural images.
Background
In recent years, a new data theory compressed sensing CS appears in the field of signal processing, the theory realizes compression while acquiring data, breaks through the limitation of the traditional nyquist acquisition Stett sampling theorem, brings revolutionary change to the data acquisition technology, and has wide application prospect in the fields of compressed imaging systems, military cryptography, wireless sensing and the like. The compressed sensing theory mainly comprises three aspects of sparse representation of signals, observation of the signals, reconstruction of the signals and the like. The design of an effective observation and reconstruction method is an important link for successfully popularizing and applying the CS theory to an actual data model and an acquisition system.
The original problem of compressed sensing reconstruction is the non-convex optimization problem with zero norm constraints. A non-convex compressed sensing image reconstruction method is proposed in the text Liu F, Lin L, Jiano L, et al, Nonconvex compressed sensing by nature, accurate optimized timing and errors [ J ]. IEEE Transactions on Cybernetics,2015,45(5):1042 and 1053. The method only judges whether the image blocks are smooth or not, and has poor reconstruction effect on the direction and texture image blocks.
Then, in the text "Lin L, Fang L, Jiano L, et al, the over-complete Directional Estimation Model and non-continuous Reconstruction method [ J ]. IEEE Transactions on Cybernetics,2017, PP (99): 1-12", a non-convex compression perception image Reconstruction method Based on a direction Estimation Model is disclosed, and the method also adopts a two-stage Reconstruction method, but before Reconstruction, the direction Estimation Model is adopted, the structure type and the direction judgment of an image are judged according to observation data, and different Dictionary Reconstruction and evolution strategies are designed according to different structure types, so that the speed of a Reconstruction algorithm is accelerated, and the accuracy of the reconstructed image is increased. Although the method judges the structure type and the direction of the image block, the method is not accurate under the condition of low sampling rate, so that the reconstruction under the low sampling rate lacks accuracy and robustness.
Meanwhile, the two methods have the defect of slow reconstruction speed, and both methods are based on two-stage optimization of a genetic optimization algorithm and a clonal selection algorithm, have slow speed and are not beneficial to real-time application.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering, aiming at the defects in the prior art, so that the reconstruction speed is increased, and the accuracy and robustness of image reconstruction under a low sampling rate are improved.
The invention adopts the following technical scheme:
the non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering defines a sketch enabling block and a non-sketch enabling block according to a sketch map of an image, wherein the non-sketch enabling block comprises a light sliding block and a texture block, and the sketch enabling block comprises a unidirectional block and a multidirectional block; the unidirectional blocks adopt clustering based on sketch direction guidance; clustering based on direction distribution characteristics is adopted for the multi-directional blocks; the light sliding block and the texture block adopt gray level clustering; carrying out multi-measurement vector observation on each type of image block; and reconstructing by adopting a particle swarm algorithm based on intersection and atom direction constraint according to the multi-measurement matrix, the category index and the direction information of each type of image block to obtain a final reconstructed image.
Preferably, the specific steps are as follows:
s1, the data sender divides the image blocks into four structural types, namely unidirectional image blocks, multidirectional image blocks, texture image blocks and smooth image blocks according to the sketch characteristics of the original image;
s2, clustering according to the direction of the unidirectional image block by adopting a clustering method based on direction guidance to obtain a clustering result of the unidirectional image block;
s3, clustering according to the sketch blocks corresponding to the multi-direction image blocks by adopting a clustering method based on direction distribution characteristics to obtain multi-direction clustering results;
s4, clustering the texture image blocks and the smooth image blocks by adopting the collected gray scale features to obtain clustering results of the texture image blocks and the smooth image blocks;
s5, adopting random Gaussian measurement matrix phi to carry out multi-measurement vector observation on each type of image block to obtain multi-measurement directionSet of quantity observation matrices { Y1,Y2...,Yi,...,YC}，YiAs the i-th type image block XiMultiple measurement vector observation matrix of, Yi＝ΦXiI ═ 1, 2., C are total classification numbers;
s6, collecting multiple measurement vector observation matrixes { Y1,Y2...,Yi,...,YCThe category index vector l ═ l (l)1,l2,...,ln,...,lN) And the direction information vector z ═ (z)1,z2,...,zi,...,zC) Is sent to a receiving party, wherein lnIs the nth image block xnClass i to whichn∈{1,2,...,C}，ziIndicating orientation information of the ith type image block if the ith type image block XiIs a smooth block, then z i0 if the i-th class image block XiIs a texture block or a multidirectional block, then ziIf the i-th class image block X is 37iIs of the unidirectional type and has a principal direction equal to theta(l)Then z isiIs equal to the index l corresponding to the main direction;
s7, the receiver judges the structure type of each image block according to the received data and constructs a corresponding over-complete redundant dictionary;
s8, searching the optimal atom combination of the particles in the direction and scale by using a particle swarm algorithm based on intersection and atom direction constraint according to the corresponding multi-measurement vector observation matrix of each type of image block under the corresponding over-complete redundant dictionary, and calculating to obtain the estimated value of the image block;
and S9, splicing the estimated values of all the image blocks into a whole reconstructed image according to the information provided by the category index vector l and outputting the reconstructed image.
Preferably, step S1 specifically includes:
s11, obtaining a sketch of the original image through the initial sketch model;
s12, dividing the sketch of the original image into non-overlapping sketch blocks with equal size, wherein the sketch block through which the sketch lines pass is called a sketch enabling block, and the image block through which no sketch line passes is called a sketch disabling block;
s13, dividing the original image block into non-overlapping and equal-size image blocks, wherein the size of each image block is the same as that of the sketch block, the image block corresponding to the sketch block is called a sketch-possible image block, and the image block corresponding to the non-sketch block is called a non-sketch image block;
s14, dividing the non-sketch image block into a smooth image block and a texture image block according to the size of each variance, wherein if the variance of the non-sketch image block is smaller than a threshold value T, the image block is a smooth image block, otherwise, the image block is a texture image block;
and S15, dividing the sketch image block into a unidirectional block and a multidirectional block according to the distribution condition of sketch line segments in the corresponding sketch block, wherein if only one sketch line segment exists in the sketch block corresponding to the sketch image block or the direction deviation between the sketch line segments does not exceed 15 degrees, the image block is a unidirectional block, the direction of the unidirectional block is the average direction of the sketch line segments in the corresponding sketch block, and otherwise, the image block is a multidirectional image block.
Preferably, step S2 specifically includes:
s21, modifying the direction of the unidirectional image block to make the direction information of the image block coincide with the direction information of the structured overcomplete ridged wave redundant dictionary, and dividing the atoms of the overcomplete ridged wave redundant dictionary into 36 directions thetal∈{θ(1),...,θ(l),...,θ(36)}，θ(l)And (l-1) pi/36, wherein l is 1,2, 36, and the direction k of the unidirectional image block is closed to 36 directions of the overcomplete ridge wave redundant dictionary to obtain the main direction of the unidirectional image block
Figure BDA0001381963440000041
Figure BDA0001381963440000042
Wherein,
Figure BDA0001381963440000043
absolute value of | represents,
Figure BDA0001381963440000044
represents | k-theta(l)Theta when | takes the minimum value(l)Taking the value of (A);
s22, dividing the unidirectional image blocks with the same main direction into a class, and dividing the unidirectional image blocks into 36 groups according to different main directions to be used as 36 sub-direction classes;
and S23, performing secondary clustering on the image blocks in each sub-direction class according to the gray scale characteristics of the image blocks to obtain a clustering result of the unidirectional image blocks.
Preferably, step S3 specifically includes:
s31, dividing the sketch blocks corresponding to the multidirectional blocks into non-overlapping statistical windows with the size of 4 multiplied by 4;
s32, obtaining the direction of each statistical window through a direction pooling operation;
s33, calculating the difference between the two image blocks according to the direction statistical distribution characteristics of the image blocks;
s34, clustering the multi-direction image blocks according to the direction statistical distribution feature vectors of the image blocks provided in the step S32 and the difference calculation method among the image blocks provided in the step S33 to obtain a first clustering result of the multi-direction blocks;
and S35, performing secondary clustering on each type of the multi-direction image blocks after the primary clustering according to the gray features of the multi-direction image blocks to obtain the final clustering result of the multi-direction image blocks.
Preferably, in step S32, the concrete operation of directional pooling is:
s321, if the sketch line in one direction only exists in the statistical window, the direction of the window is the direction corresponding to the sketch line;
s322, if a statistical window comprises sketch lines in a plurality of directions, taking the direction of the longest sketch line segment in a 4 x 4 statistical window as the direction of the window, and taking the number of pixels of the sketch line segment in the statistical window as the length of the sketch line segment;
in step S33, the difference between the two image blocks is specifically:
s331, calculating a direction statistical distribution characteristic vector beta of the a-th image blockaAnd the direction statistical distribution characteristic vector beta of the b-th image blockbAngle difference vector D (β) therebetweena，βb)：
Figure BDA0001381963440000051
Figure BDA0001381963440000052
Wherein,
Figure BDA0001381963440000053
is shown asaIn a block of an imagejThe direction of the individual statistical windows is such that,
Figure BDA0001381963440000054
is shown asbIn a block of an imagejThe direction of the individual statistical windows is such that,
Figure BDA0001381963440000055
represents the angular difference vector D (beta)a，βb) To (1) ajA component;
s332, calculating the difference between the two image blocks according to the angle difference vector between the two angle direction statistical distribution feature vectors:
Figure BDA0001381963440000056
preferably, step S7 specifically includes:
s71, if the orientation information z of the ith class image blockiIf 0, the class is a smooth image block class, and the corresponding smooth overcomplete redundant dictionary is ΨsThe overcomplete dictionary is composed of ridge redundancy sub-dictionaries of the first 5 scales of all directions in the ridge redundancy dictionary,
Figure BDA0001381963440000061
Figure BDA0001381963440000062
representing a ridge wave redundant sub-dictionary containing all directions with a scale h, wherein h is 1, 2.
S72, if the orientation information z of the ith class image blockiE {1, 2.., 36}, then the class is smooth image block class, ziCorresponding to the index l corresponding to the main direction of the image block, and taking out the main direction theta of the single-side block(l)And the sub-dictionaries of 4 directions adjacent to the left and right of the main direction are used as the overcomplete redundant dictionary of the unidirectional block;
s73, if the orientation information z of the ith class image blockiAnd if the class is 37, the class is a texture image block class or a multi-direction image block class, and the whole ridge wave overcomplete redundant dictionary is used as an overcomplete redundant dictionary of the class.
Preferably, step S8 specifically includes:
s81, initializing particle swarm;
s82, solving the speed of atom direction constraint;
s83, the particle position is according to the particle update probability PrUpdating, wherein the updating operation is the addition of the current particle position and the controlled particle speed;
s84, calculating a new fitness value of the updated particles, if the new fitness value of the particles is larger than the fitness value of the last iteration of the particles, replacing the current particles with the updated particles, sequencing atoms on each particle from small to large according to atom numbers, otherwise, keeping the particles unchanged, and rearranging the speed of the updated particles according to indexes of the sequenced atoms on the particles to enable each dimension of the position of each particle to correspond to the speed of the particle one to one;
s85, using the particle swarm currently moving as a to-be-crossed population, performing a single-point crossing operation, and setting a probability Pc, where the crossing probability Pc of a unidirectional image block class and a smooth block class is 0.5, and the crossing probability Pc of a multidirectional image block class and a texture image block class is 0.6; selecting one particle with larger fitness from the two new child particles, and comparing the fitness value with the fitness values of the two parent particles generating the particle:
if the fitness value of the parent particle is large, replacing the parent particle, sequencing the atoms on each crossed particle from small to large according to the atom numbers, rearranging the respective speeds according to the indexes after the atoms on the particles are sequenced, and otherwise, not replacing;
s86, updating the historical optimal position and the global historical optimal position of the particles in the particles;
s87, judging whether the iteration stop condition of the particle swarm optimization is met, if so, executing the step S88, if not, returning to the step S82, and continuing to perform speed and position updating operation on the particles;
s88, taking the global historical optimal solution of the particle swarm as a reconstruction base of the image block;
s89, obtaining the optimal atomic combinations of all the image blocks, and calculating the estimated values x of all the image blocks by the following formulan：
xn＝Dn[(ΦDn)+yn]
Wherein D isnRepresenting the most atomic combination of the image block, ynAn observation vector representing the image block.
Preferably, step S81 specifically includes:
s811, for each type of unidirectional image block, according to the overcomplete redundant dictionary ΨgInitializing a particle group with the size of 20, dividing the particle group into 5 groups, each group representing a direction, randomly initializing particles in each group, arranging atoms on each particle in order from small to large according to atom numbers, and randomly initializing the velocity of the particles to [ -L ]r,Lr]Any value of x 0.5, wherein LrThe size of a sub-dictionary corresponding to the direction r in the single-direction class overcomplete redundant dictionary belongs to {1, 2.., 36 };
s812, initializing a particle group with the size of 36 for the texture image block class and the multi-direction image block class, wherein each particle represents twoSelecting one direction from the ridge wave overcomplete redundant dictionary to be the same as the particle number, randomly selecting one direction from the rest directions in the other direction, orderly arranging atoms on each particle from small to large according to the original number, and randomly initializing the particle speed to be [ -L ]m,Lm]Any value of x 0.5, wherein LmA size of an overcomplete ridge redundancy dictionary representing two selected representative directions, m representing a particle number, m being 1, 2.
S813, calculating the fitness value of each particle in the group of smooth image blocks, one-way image blocks, texture image blocks and multi-direction image blocks according to the following formula:
Figure BDA0001381963440000081
wherein, f (b)m) The fitness value Y of the m-th particle in the particle swarm of the image block corresponding to the multi-measurement matrix of the classiRepresenting image block X of class iiMultiple measurement vector observation matrix of, bmIs a solution represented by the m-th particle in the particle swarm, corresponding to a group of base atom combinations in the ridge overcomplete redundant dictionary, (. DEG)+A pseudo-inverse matrix representing a computational matrix,
Figure BDA0001381963440000082
represents the square of the matrix Frobenius norm;
s814, initializing a historical optimal solution and a global historical optimal solution of the particle swarm: initializing the historical optimal solution of each particle in the particle swarm into the particle, and taking the particle with the maximum fitness value in the whole particle swarm as the global historical optimal solution.
Preferably, step S82 specifically includes:
s821, setting parameters in the particle swarm algorithm, and updating the particle velocity position of the particle swarm as follows:
Figure BDA0001381963440000083
wherein,
Figure BDA0001381963440000084
represents the speed corresponding to the u component of the m particle after the t +1 th iteration updating,
Figure BDA0001381963440000085
a u-th component representing a corresponding velocity of an m-th particle in the current particle population,
Figure BDA0001381963440000086
representing the u-th component of the m-th particle in the current particle population,
Figure BDA0001381963440000087
the u-th component of the historical optimal position of the m-th particle in the current particle population,
Figure BDA0001381963440000088
represents the current global historical optimal position gtU is a positive integer, t denotes the current iteration, w denotes the inertial weight, c1Weight coefficient representing historical optimum value of particle tracking itself, c2Weight coefficient representing optimal value of particle tracking global history, and xi and eta are [0, 1]Two random numbers uniformly distributed in the interval;
s822, firstly, according to each current particle dimension component
Figure BDA0001381963440000089
R in the direction of the atom in (b), the atomic range [ g ] of the r-th direction is obtainedr,hr](ii) a Then, the direction constraint is carried out on the speed of the particles according to the following formula to obtain the controlled speed of the particles
Figure BDA00013819634400000810
Figure BDA00013819634400000811
Compared with the prior art, the invention has at least the following beneficial effects:
the invention relates to a non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering, which is characterized in that accurate structural type, category and direction information of image blocks are obtained according to a structured clustering method based on sketch representation, the information and multivariable observation results of each type of image blocks are sent to a receiving party together, so that the receiving party can improve the accuracy of image reconstruction, and a particle swarm algorithm based on intersection and atomic direction constraint is adopted to reconstruct according to multiple measurement matrixes, category indexes and direction information of each type of image blocks to obtain a final reconstructed image.
Furthermore, the image blocks are classified according to the sketch characteristics of the original image before observation, the structural features of the image blocks are fully mined, compared with the prior art that the structural features of the image blocks are extracted according to the observation results, the obtained structural features of the image blocks are more accurate, the structural types, the categories and the direction information of the image blocks and each type of multivariable observation results are sent to a receiving party together, and the accurate prior information can accurately guide the receiving party to effectively reconstruct the image, so that the quality and the robustness of image reconstruction are improved.
Furthermore, the mean square error of the gray values of the image blocks including the edges in the natural image blocks and the gray values of the smooth image blocks are low, and the image blocks are difficult to be divided through a threshold.
Furthermore, a clustering method based on direction distribution characteristics is provided, so that multi-direction image blocks of the same class have similar direction structure characteristics, different clustering methods are designed for image blocks of different structure types according to corresponding sketch blocks, a gray-scale-based clustering method is adopted for optical sliding blocks and texture blocks, a direction-guidance-based clustering method is adopted for unidirectional blocks, and a direction distribution characteristic-based clustering method is adopted for multi-direction image blocks, so that the image blocks in the same class have similar direction structure characteristics.
Furthermore, the particle swarm algorithm based on the cross and atom direction constraints is used for searching the optimal atom combination of the particles in the direction and the scale, the estimation value of the image block is obtained through calculation, the particle swarm algorithm based on the cross and courtyard direction constraints is provided during the optimization solution, and the optimization solution speed is improved.
Furthermore, the particle swarm algorithm is adopted, and the image reconstruction speed is improved.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a schematic diagram of a multi-directional block image block with directional statistical distribution;
fig. 3 is a graph showing the results of the reconstruction of barbarbara plots at 20% sampling rate according to the present invention and two conventional methods, respectively, wherein (a) is an original barbarbarbara plot, (b) is a partial enlarged view of plot a, (c) is a reconstructed plot obtained by a two-stage reconstruction method, (d) is a partial enlarged view of plot (c), (e) is a reconstructed plot obtained by a direction-oriented reconstruction, (f) is a partial enlarged view of plot e, (g) is a reconstructed plot obtained according to the present invention, and (h) is a partial enlarged view of plot g;
fig. 4 is a graph of the reconstruction results of Lena images at 20% sampling rate according to the present invention and two conventional methods, wherein (a) is Lena original image, (b) is a partial enlarged view of the image a, (c) is a reconstructed image obtained by a two-stage reconstruction method, (d) is a partial enlarged view of the image c, (e) is a reconstructed image obtained by direction-guided reconstruction, (f) is a partial enlarged view of the image e, (g) is a reconstructed image obtained by the present invention, and (h) is a partial enlarged view of the image g;
fig. 5 is a time line graph of the reconstruction of Lena plots at different sampling rates for the present invention and for two prior art methods.
Detailed Description
The invention provides a non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering, wherein a sketch enabling block and a sketch disabling block are defined according to a sketch map of an image, wherein the sketch disabling block comprises an optical sliding block and a texture block, and the sketch enabling block comprises a unidirectional block and a multidirectional block; the unidirectional blocks adopt clustering based on sketch direction guidance; clustering based on direction distribution characteristics is adopted for the multi-directional blocks; the light sliding block and the texture block adopt gray level clustering; carrying out multi-measurement vector observation on each type of image block; during reconstruction, a final reconstructed image is obtained by adopting a particle swarm algorithm based on intersection and atom direction constraint according to the multi-measurement matrix, the category index and the direction information of each type of image block.
Referring to fig. 1, the non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering of the present invention specifically includes the following steps:
and S1, the data sender divides the image blocks into four different structure types, namely unidirectional image blocks, multidirectional image blocks, texture image blocks and smooth image blocks according to the sketch characteristics of the original image, and the directions of the unidirectional image blocks can be obtained when the structure types are divided.
S11, obtaining a sketch of the original image through the initial sketch model;
s12, dividing the sketch of the original image into non-overlapping sketch blocks with equal size, wherein the sketch block through which the sketch lines pass is called a sketch enabling block, and the image block through which no sketch line passes is called a sketch disabling block;
s13, dividing the original image block into non-overlapping and equal-size image blocks, wherein the size of each image block is the same as that of the sketch block, the image block corresponding to the sketch block is called a sketch-possible image block, and the image block corresponding to the non-sketch block is called a non-sketch image block;
s14, dividing the non-sketch image block into a smooth image block and a texture image block according to the size of each variance, wherein if the variance of the non-sketch image block is smaller than a threshold value T, the image block is a smooth image block, otherwise, the image block is a texture image block;
and S15, dividing the sketch image block into a unidirectional block and a multidirectional block according to the distribution condition of sketch line segments in the corresponding sketch block, wherein if only one sketch line segment exists in the sketch block corresponding to the sketch image block or the direction deviation between the sketch line segments does not exceed 15 degrees, the image block is a unidirectional block, the direction of the unidirectional block is the average direction of the sketch line segments in the corresponding sketch block, and otherwise, the image block is a multidirectional image block.
S2, clustering the unidirectional image blocks by adopting a clustering method based on direction guidance according to the directions of the unidirectional image blocks to obtain clustering results of the unidirectional image blocks;
s21, modifying the direction of the unidirectional image block to make the direction information of the image block coincide with the direction information of the structured overcomplete ridged wave redundant dictionary, wherein the atoms of the overcomplete ridged wave redundant dictionary can be divided into 36 directions
Figure BDA0001381963440000111
θ(l)And (l-1) pi/36, wherein l is 1,2, 36, and the direction k of the unidirectional image block is closed to 36 directions of the overcomplete ridge wave redundant dictionary to obtain the main direction of the unidirectional image block
Figure BDA0001381963440000112
Figure BDA0001381963440000121
Wherein,
Figure BDA0001381963440000122
absolute value of | represents,
Figure BDA0001381963440000123
represents | k-theta(l)Theta when | takes the minimum value(l)Taking the value of (A);
s22, dividing the unidirectional image blocks with the same main direction into one type, so that the unidirectional image blocks are divided into 36 groups according to different main directions, and the unidirectional image blocks are called as 36 sub-direction types;
and S23, performing secondary clustering on the image blocks in each sub-direction class according to the gray scale characteristics of the image blocks to obtain a clustering result of the unidirectional image blocks.
S3, clustering the multi-directional image blocks according to the corresponding sketch blocks by adopting a clustering method based on directional distribution characteristics to obtain multi-directional clustering results, as shown in FIG. 2, the specific process is as follows;
s31, dividing the sketch blocks corresponding to the multidirectional blocks into non-overlapping statistical windows with the size of 4 multiplied by 4;
s32, obtaining the direction of each statistical window through a direction pooling operation, wherein the direction pooling operation comprises the following specific operations:
s321, if the sketch line in one direction only exists in the statistical window, the direction of the window is the direction corresponding to the sketch line;
s322, if a statistical window comprises sketch lines in a plurality of directions, taking the direction of the longest sketch line segment in a 4 x 4 statistical window as the direction of the window, and taking the number of pixels of the sketch line segment in the statistical window as the length of the sketch line segment;
the directions of all statistical windows in the sketch block form a direction statistical distribution characteristic vector beta of the corresponding image block1,...,βj...,βJ]Wherein beta isjIs the direction of the jth statistical window in the corresponding image block, J is the number of statistical windows in each image block, if no sketch line passes through in the jth window, the corresponding beta isj＝0；
S33, calculating the difference between the two image blocks according to the direction statistical distribution characteristics of the image blocks:
s331, calculating a direction statistical distribution characteristic vector beta of the a-th image blockaAnd a firstbDirection statistical distribution characteristic vector beta of each image blockbAngle difference vector D (β) therebetweena，βb)：
Figure BDA0001381963440000124
Figure BDA0001381963440000131
Wherein,
Figure BDA0001381963440000132
is shown asaIn a block of an imagejThe direction of the individual statistical windows is such that,
Figure BDA0001381963440000133
is shown asbIn a block of an imagejThe direction of the individual statistical windows is such that,
Figure BDA0001381963440000134
represents the angular difference vector D (beta)a，βb) To (1) ajA component;
s332, calculating the difference between the two image blocks according to the angle difference vector between the two angle direction statistical distribution feature vectors
Figure BDA0001381963440000135
Wherein the difference diff (beta) between two image blocksa，βb) The smaller the similarity between the two image blocks is, the higher the similarity between the two image blocks is;
s34, clustering the multi-direction image blocks according to the direction statistical distribution feature vectors of the image blocks provided in the step S32 and the difference calculation method among the image blocks provided in the step S33 to obtain a first clustering result of the multi-direction blocks;
and S35, performing secondary clustering on each type of the multi-direction image blocks after the primary clustering according to the gray features of the multi-direction image blocks to obtain the final clustering result of the multi-direction image blocks.
S4, clustering the texture image blocks and the smooth image blocks by using the clustering of the aggregation gray scale features to obtain clustering results of the texture image blocks and the smooth image blocks;
s5, adoptCarrying out multi-measurement vector observation on each type of image block by using a random Gaussian measurement matrix phi to obtain a multi-measurement vector observation matrix set { Y }1,Y2...,Yi,...,YC}，YiAs the i-th type image block XiMultiple measurement vector observation matrix of, Yi＝ΦXiI ═ 1, 2., C are total classification numbers;
s6, collecting multiple measurement vector observation matrixes { Y1,Y2...,Yi,...,YCThe category index vector l ═ l (l)1,l2,...,ln,...,lN) Wherein l isnIs the nth image block xnClass i to whichnE {1, 2.., C }, and a direction information vector z ═ z (z ═ z ·)1,z2,...,zi,...,zC) Is sent to a receiving party, wherein ziIndicating orientation information of the ith type image block if the ith type image block XiIs a smooth block, then z i0 if the i-th class image block XiIs a texture block or a multidirectional block, then ziIf the i-th class image block X is 37iIs of the unidirectional type and has a principal direction equal to theta(l)Then z isiEqual to the index l corresponding to the main direction.
S7, the receiver judges the structure type of each image block according to the received data, and constructs a corresponding overcomplete redundant dictionary:
s71, if the orientation information z of the ith class image blockiIf 0, the class is a smooth image block class, and the corresponding smooth overcomplete redundant dictionary is ΨsThe overcomplete dictionary is composed of ridge redundancy sub-dictionaries of the first 5 scales of all directions in the ridge redundancy dictionary,
Figure BDA0001381963440000141
Figure BDA0001381963440000142
representing a ridge wave redundant sub-dictionary containing all directions with a scale h, wherein h is 1, 2.
S72, if the orientation information z of the ith class image blocki∈{1,2,...,36} then the class is smooth image block class, ziCorresponding to the index l corresponding to the main direction of the image block, and taking out the main direction theta of the single-side block(l)And the sub-dictionaries of 4 directions adjacent to the left and right of the main direction are used as the overcomplete redundant dictionary of the unidirectional block;
s73, if the orientation information z of the ith class image blockiAnd if the class is 37, the class is a texture image block class or a multi-direction image block class, and the whole ridge wave overcomplete redundant dictionary is used as an overcomplete redundant dictionary of the class.
And S8, searching the optimal atom combination of the particles in the direction and scale by using a particle swarm algorithm based on intersection and atom direction constraint according to the corresponding multi-measurement vector observation matrix of each type of image block under the corresponding over-complete redundant dictionary, and calculating to obtain the estimated value of the image block.
S81 initializing particle group
S811, for each type of unidirectional image block, according to the overcomplete redundant dictionary ΨgInitializing a particle group with the size of 20, dividing the particle group into 5 groups, each group representing a direction, randomly initializing particles in each group, arranging atoms on each particle in order from small to large according to atom numbers, and randomly initializing the velocity of the particles to [ -L ]r,Lr]Any value of x 0.5, wherein LrThe size of a sub-dictionary corresponding to the direction r in the single-direction class overcomplete redundant dictionary belongs to {1, 2.., 36 };
s812, initializing a particle swarm with the scale of 36 for texture image blocks and multidirectional image blocks, wherein each particle represents two directions, one direction selects the direction with the same number as the particle from a ridge wave overcomplete redundant dictionary, the other direction selects one direction from the rest directions again randomly, atoms on each particle are arranged from small to large according to the original number, and then the speed of the particle is initialized to [ -L ] randomlym,Lm]Any value of x 0.5, wherein LmSize of overcomplete ridge redundancy dictionary representing two selected representative directions, m-tableIndicates the particle number, m 1, 2.., 36;
s813, calculating the fitness value of each particle in the group of smooth image blocks, one-way image blocks, texture image blocks and multi-direction image blocks according to the following formula:
Figure BDA0001381963440000151
wherein, f (b)m) The fitness value of the m-th particle in the particle swarm of the image block corresponding to the multi-measurement matrix of the class, bmIs a solution represented by the m-th particle in the particle swarm, corresponding to a group of base atom combinations in the ridge overcomplete redundant dictionary, (. DEG)+A pseudo-inverse matrix representing a computational matrix,
Figure BDA0001381963440000152
represents the square of the matrix Frobenius norm;
s814, initializing a historical optimal solution and a global historical optimal solution of the particle swarm: initializing the historical optimal solution of each particle in the particle swarm into the particle, and taking the particle with the maximum fitness value in the whole particle swarm as a global historical optimal solution;
s82 velocity solution of atom direction constraint
S821, setting parameters in the particle swarm algorithm, and updating the particle velocity position of the particle swarm as follows:
Figure BDA0001381963440000153
wherein,
Figure BDA0001381963440000154
represents the speed corresponding to the u component of the m particle after the t +1 th iteration updating,
Figure BDA0001381963440000155
a u-th component representing a corresponding velocity of an m-th particle in the current particle population,
Figure BDA0001381963440000156
representing the u-th component of the m-th particle in the current particle population,
Figure BDA0001381963440000157
the u-th component of the historical optimal position of the m-th particle in the current particle population,
Figure BDA0001381963440000158
represents the current global historical optimal position gtU is a positive integer, the maximum value is equal to the set sparsity, t represents that the current iteration is the number of times, represents the w inertial weight, w decreases linearly from 0.9 to 0.4, c1Weight coefficient representing historical optimum value of particle tracking itself, c1Linear decrease from 2.5 to 0.5, c2Weight coefficient representing the optimal value of the particle tracking global history, c2Linearly increasing from 0.5 to 2.5, xi and eta are [0, 1 ]]Two random numbers uniformly distributed in the interval;
adding a particle position updating probability parameter Pr，PrLinearly decreasing from 1.0 to 0.1 with evolution algebra;
s822, firstly, according to each current particle dimension component
Figure BDA0001381963440000161
R in the direction of the atom in (b), the atomic range [ g ] of the r-th direction is obtainedr,hr](ii) a Then, the direction constraint is carried out on the speed of the particles according to the following formula to obtain the controlled speed of the particles
Figure BDA0001381963440000162
Figure BDA0001381963440000163
S83, the particle position is according to the particle update probability PrPerforming an update, wherein the update operation is the current particle position plus the controlled particle velocity；
S84, calculating a new fitness value of the updated particles, if the new fitness value of the particles is larger than the fitness value of the last iteration of the particles, replacing the current particles with the updated particles, sequencing atoms on each particle from small to large according to atom numbers, otherwise, keeping the particles unchanged, and rearranging the speed of the updated particles according to indexes of the sequenced atoms on the particles to enable each dimension of the position of each particle to correspond to the speed of the particle one to one;
s85, using the particle swarm currently moving as a to-be-crossed population, executing single-point cross operation, and setting the probability as Pc, wherein the cross probability Pc of a unidirectional image block class and a smooth block class is 0.5, and the cross probability Pc of a multidirectional image block class and a texture image block class is 0.6; selecting one particle with larger fitness from the two new child particles, and comparing the fitness value with the fitness values of the two parent particles generating the particle: if the fitness value of the parent particle is large, replacing the parent particle, sequencing the atoms on each crossed particle from small to large according to the atom numbers, rearranging the respective speeds according to the indexes after the atoms on the particles are sequenced, and otherwise, not replacing;
s86, updating the historical optimal position and the global historical optimal position of the particles in the particles;
s87, judging whether the iteration stop condition of the particle swarm optimization is met, if so, executing the step S88, if not, returning to the step S82, and continuing to perform speed and position updating operation on the particles;
and S88, taking the global historical optimal solution of the particle swarm as a reconstruction base of the image block of the type.
And S89, calculating the estimated values of all the image blocks by the following formula according to the obtained optimal atomic combination of all the image blocks:
xn＝Dn[(ΦDn)+yn]
wherein D isnRepresenting the most atomic combination of the image block, y representing the image blocknAnd observing the vector.
And S9, splicing the estimated values of all the image blocks into a whole reconstructed image according to the information provided by the category index vector l and outputting the reconstructed image.
Examples
1. Simulation conditions are as follows: the simulation of the invention runs on windows 7, SPI, CPU Intel (R) core (TM) i5-3470 and the fundamental frequency is 3.20GHz, the software platform is Matlab R2011b, and four standard test natural images Lena, Barbara and Boat of 512 multiplied by 512 are selected for simulation, and the size of blocks is small.
2. Simulation content and results:
simulation 1:
fig. 3 shows simulation results obtained by reconstructing a Barbara image by the method of the present invention and a conventional method under a condition of a sampling rate of 20%, where fig. 3(a) is an original Barbara image, fig. 3(b) is a partial enlarged view of fig. 3(a), fig. 3(c) is a reconstructed image obtained by a two-stage reconstruction method (TS _ RS), fig. 3(d) is a partial enlarged view of fig. 3(c), fig. 3(e) is a reconstructed image obtained by a direction-directed reconstruction (NR _ DG), fig. 3(f) is a partial enlarged view of fig. 3(e), fig. 3(g) is a reconstructed image obtained by the present invention, and fig. 3(h) is a partial enlarged view of fig. 3 (g).
Compared with the reconstructed patterns of TS _ RS and NR _ DG, FIG. 3(g) of the present invention is more similar to FIG. 3(a) of the original drawing, and the corresponding partial enlarged view is compared, and FIG. 3(h) is more clearly reconstructed than FIG. 3(d), FIG. 3(h) and the texture on the Barbara trouser legs.
The experimental results of fig. 3 demonstrate that the reconstructed image obtained using the method of the present invention is visually superior to the reconstructed image obtained using the two-stage reconstruction method and the direction-guided reconstruction method. From comparison of the partial enlarged images, the texture reconstruction method provided by the invention can be used for reconstructing the texture on the Barbara trouser legs more clearly, and the method is used for reconstructing the edge and unidirectional texture image blocks of the images more accurately.
Simulation 2:
fig. 4 shows a simulation result diagram in which Lena images are reconstructed by the method of the present invention and the conventional method under the condition of a sampling rate of 20%, where fig. 4(a) is a Lena original image, fig. 4(b) is a partial enlarged view of fig. 4(a), fig. 4(c) is a reconstructed image obtained by a two-stage reconstruction method (TS _ RS), fig. 4(d) is a partial enlarged view of fig. 4(c), fig. 4(e) is a reconstructed image obtained by a direction-directed reconstruction (NR _ DG), fig. 4(f) is a partial enlarged view of fig. 4(e), fig. 4(g) is a reconstructed image obtained by the present invention, and fig. 4(h) is a partial enlarged view of fig. 4 (g).
Compared with the reconstructed images of TS _ RS and NR _ DG, 4(c) and 4(e) of the reconstructed images of TS _ RS and NR _ DG, the reconstructed image of the invention is more similar to that of the original image 4(a), and compared with the corresponding partial enlarged image, 4(h) is clearer than that of 4(d) and 4(h), the edge of the Lena shoulder part is more clear, and the smooth part has better consistency.
As can be seen from FIG. 4, the edge of the shoulder part of Lena is clearer and the smooth part has better consistency than the reconstructed image obtained by the reconstruction method of the two-stage reconstruction method and the direction guidance, which shows that the reconstructed image has better reconstruction performance for the natural image.
Simulation 3
At different sampling rates, Lena, Barbar and Boat maps were reconstructed using the method of the present invention and the prior art method, respectively, and the numerical results obtained were compared in the on-line manner, and the results are shown in table 1.
As can be seen from Table 1, the PSNR and SSIM values of the reconstructed image are higher than those of a two-stage reconstruction method (TS _ RS) and a direction-guided reconstruction method (NR _ DG), which shows that the reconstructed image has better reconstruction performance on natural images.
Table 1 shows the results of the PSNR (structural similarity SSIM) indexes of the image peak signal-to-noise ratios in the three methods
Figure BDA0001381963440000181
Figure BDA0001381963440000191
Fig. 5 is a time line graph of reconstruction of Lena graph under different sampling rates by the present invention and two existing methods, and it can be seen that the triangular line representing the present invention is located under the other two methods, which shows that the reconstruction time required by the present invention is the shortest under each sampling rate, and further shows that the present invention has a faster reconstruction speed to nature.
In conclusion, clear reconstructed images can be well obtained under the sampling and reconstruction method provided by the invention, and compared with the existing observation and reconstruction method, the method provided by the invention improves the reconstruction quality and reconstruction speed of the images.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (5)

1. The non-convex compressed sensing optimization reconstruction method based on sketch representation and structured clustering is characterized in that a sketch block and a non-sketch block are defined according to a sketch map of an image, the sketch block with a sketch line passing through is called the sketch block, the sketch block without the sketch line passing through is called the non-sketch block, an original image block is divided into image blocks with non-overlapping equal size, the size of the image block is the same as that of the sketch block, the image block corresponding to the sketch block is called the sketch block, the image block corresponding to the non-sketch block is called the non-sketch image block, the non-sketch image block comprises a smooth image block and a texture image block according to the size of respective variance, if the variance of the non-sketch image block is smaller than a threshold value T, the image block is a smooth image block, otherwise, the image block is a texture image block, the sketch image block comprises a unidirectional multidirectional image block and an image block, if only one line drawing segment exists in the line drawing blocks corresponding to the line drawing image blocks or the direction deviation between the line drawing segments does not exceed 15 degrees, the image blocks are unidirectional image blocks, the direction of the unidirectional image blocks is the average direction of the line drawing segments in the corresponding line drawing blocks, and otherwise, the image blocks are multidirectional image blocks; clustering the unidirectional image blocks based on sketch direction guidance; clustering the multi-directional image blocks based on direction distribution characteristics; adopting gray level clustering for the smooth image blocks and the texture image blocks; carrying out multi-measurement vector observation on each type of image block; reconstructing by adopting a particle swarm algorithm based on intersection and atom direction constraint according to the multi-measurement matrix, the category index and the direction information of each type of image block to obtain a final reconstructed image, and specifically comprising the following steps:
s1, the data sender divides the image block into four structural types of a unidirectional image block, a multidirectional image block, a texture image block and a smooth image block according to the sketch characteristics of the original image, and specifically comprises the following steps:
s11, obtaining a sketch of the original image through the initial sketch model;
s12, dividing the sketch of the original image into non-overlapping sketch blocks with equal size, wherein the sketch blocks through which sketch lines pass are called sketch enabling blocks, and the sketch blocks through which sketch lines do not pass are called sketch disabling blocks;
s13, dividing the original image block into non-overlapping and equal-size image blocks, wherein the size of each image block is the same as that of the sketch block, the image block corresponding to the sketch block is called a sketch-possible image block, and the image block corresponding to the non-sketch block is called a non-sketch image block;
s14, dividing the non-sketch image block into a smooth image block and a texture image block according to the size of each variance, wherein if the variance of the non-sketch image block is smaller than a threshold value T, the image block is a smooth image block, otherwise, the image block is a texture image block;
s15, dividing the sketch image block into a unidirectional image block and a multidirectional image block according to the distribution condition of sketch line segments in the corresponding sketch block, wherein if only one sketch line segment is in the sketch block corresponding to the sketch image block or the direction deviation between the sketch line segments does not exceed 15 degrees, the image block is a unidirectional image block, the direction of the unidirectional image block is the average direction of the sketch line segments in the corresponding sketch block, otherwise, the image block is a multidirectional image block;
s2, clustering according to the direction of the unidirectional image block by adopting a clustering method based on direction guidance to obtain a clustering result of the unidirectional image block, which specifically comprises the following steps:
s21, modifying the direction of the unidirectional image block to make the direction information of the image block coincide with the direction information of the structured overcomplete ridge wave redundant dictionaryAnd dividing atoms of the overcomplete ridge wave redundant dictionary into 36 directions thetal∈{θ(1),...,θ(l),...,θ(36)}，θ(l)And (l-1) pi/36, wherein l is 1,2, 36, and the direction k of the unidirectional image block is closed to 36 directions of the overcomplete ridge wave redundant dictionary to obtain the main direction of the unidirectional image block
Figure FDA0002740690520000021
Figure FDA0002740690520000022
Wherein,
Figure FDA0002740690520000023
| represents the absolute value of · s,
Figure FDA0002740690520000024
represents | k-theta(l)Theta when | takes the minimum value(l)Taking the value of (A);
s22, dividing the unidirectional image blocks with the same main direction into a class, and dividing the unidirectional image blocks into 36 groups according to different main directions to be used as 36 sub-direction classes;
s23, carrying out secondary clustering on the image blocks in each sub-direction type according to the gray scale characteristics of the image blocks to obtain a clustering result of the unidirectional image blocks;
s3, clustering is carried out according to the sketch blocks corresponding to the multi-direction image blocks by adopting a clustering method based on direction distribution characteristics to obtain clustering results of the multi-direction image blocks, and the method specifically comprises the following steps:
s31, dividing the sketch blocks corresponding to the multi-direction image blocks into non-overlapping statistical windows with the size of 4 multiplied by 4;
s32, obtaining the direction of each statistical window through a direction pooling operation, wherein the direction pooling operation comprises the following specific operations:
s321, if the sketch line in one direction only exists in the statistical window, the direction of the window is the direction corresponding to the sketch line;
s322, if a statistical window comprises sketch lines in a plurality of directions, taking the direction of the longest sketch line segment in a 4 x 4 statistical window as the direction of the window, and taking the number of pixels of the sketch line segment in the statistical window as the length of the sketch line segment;
s33, calculating the difference between the two image blocks according to the direction statistical distribution characteristics of the image blocks specifically:
s331, calculating a direction statistical distribution characteristic vector beta of the a-th image blockaAnd the direction statistical distribution characteristic vector beta of the b-th image blockbAngle difference vector D (β) therebetweena，βb)：
Figure FDA0002740690520000031
Figure FDA0002740690520000032
Wherein,
Figure FDA0002740690520000033
is shown asaIn a block of an imagejThe direction of the individual statistical windows is such that,
Figure FDA0002740690520000034
is shown asbIn a block of an imagejThe direction of the individual statistical windows is such that,
Figure FDA0002740690520000035
represents the angular difference vector D (beta)a，βb) To (1) ajComponent, J is the number of statistical windows in each image block;
s332, calculating the difference between the two image blocks according to the angle difference vector between the two angle direction statistical distribution feature vectors:
Figure FDA0002740690520000036
s34, clustering the multi-direction image blocks according to the direction statistical distribution feature vectors of the image blocks provided in the step S32 and the difference calculation method among the image blocks provided in the step S33 to obtain a first clustering result of the multi-direction image blocks;
s35, performing secondary clustering on each type of the multi-direction image blocks after the primary clustering according to the gray features of the multi-direction image blocks to obtain final clustering results of the multi-direction image blocks;
s4, clustering the texture image blocks and the smooth image blocks by adopting the collected gray scale features to obtain clustering results of the texture image blocks and the smooth image blocks;
s5, carrying out multi-measurement vector observation on each type of image block by adopting a random Gaussian measurement matrix phi to obtain a multi-measurement vector observation matrix set { Y }1,Y2...,Yi,...,YC}，YiAs the i-th type image block XiMultiple measurement vector observation matrix of, Yi＝ΦXiI 1,2, C is the total number of categories;
s6, collecting multiple measurement vector observation matrixes { Y1,Y2...,Yi,...,YCThe category index vector l ═ l (l)1,l2,...,ln,...,lN) And the direction information vector z ═ (z)1,z2,...,zi,...,zC) Is sent to a receiving party, wherein lnIs the nth image block xnClass to which N is the total number of image blocks, ln∈{1,2,...,C}，ziIndicating orientation information of the ith type image block if the ith type image block XiFor a smooth image block, then zi0 if the i-th class image block XiFor texture image blocks or multi-directional image blocks, then ziIf the i-th class image block X is 37iIs a unidirectional image block, and the main direction is equal to theta(l)Then z isiEqual to the index vector l corresponding to the principal direction;
s7, the receiver judges the structure type of each image block according to the received data and constructs a corresponding over-complete redundant dictionary;
s8, searching the optimal atom combination of the particles in the direction and scale by using a particle swarm algorithm based on intersection and atom direction constraint according to the corresponding multi-measurement vector observation matrix of each type of image block under the corresponding over-complete redundant dictionary, and calculating to obtain the estimated value of the image block;
and S9, splicing the estimated values of all the image blocks into a whole reconstructed image according to the information provided by the category index vector l and outputting the reconstructed image.
2. The non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering according to claim 1, wherein the step S7 specifically comprises:
s71, if the orientation information z of the ith class image blockiIf 0, the class is a smooth image block class, and the corresponding smooth overcomplete redundant dictionary is ΨsThe overcomplete redundant dictionary is composed of ridge redundant sub-dictionaries of the first 5 scales of all directions in the ridge redundant dictionary,
Figure FDA0002740690520000041
Figure FDA0002740690520000042
representing a ridge wave redundant sub-dictionary containing all directions with a scale h, wherein h is 1, 2.
S72, if the orientation information z of the ith class image blockiE {1, 2.., 36}, the class is a unidirectional image block class, ziCorresponding to the index l corresponding to the main direction of the image block, and taking out the main direction theta of the unidirectional image block(l)And the sub-dictionaries of 4 directions adjacent to the left and right of the main direction are used as the over-complete redundant dictionary of the unidirectional image block;
s73, if the orientation information z of the ith class image blockiIf the class is 37, the class is a texture image block class or a multidirectional image block class, and the whole ridge wave overcomplete redundant dictionary is used as an overcomplete redundant word of the classA dictionary is also provided.
3. The non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering according to claim 1, wherein the step S8 specifically comprises:
s81, initializing particle swarm;
s82, solving the speed of atom direction constraint;
s83, the particle position is according to the particle update probability PrUpdating, wherein the updating operation is the addition of the current particle position and the controlled particle speed;
s84, calculating a new fitness value of the updated particles, if the new fitness value of the particles is larger than the fitness value of the last iteration of the particles, replacing the current particles with the updated particles, sequencing atoms on each particle from small to large according to atom numbers, otherwise, keeping the particles unchanged, and rearranging the speed of the updated particles according to indexes of the sequenced atoms on the particles to enable each dimension of the position of each particle to correspond to the speed of the particle one to one;
s85, using the particle swarm currently moving as a to-be-crossed population, performing a single-point crossing operation, and setting a probability Pc, where the crossing probability Pc of the unidirectional image block class and the smooth image block class is 0.5, and the crossing probability Pc of the multidirectional image block class and the texture image block class is 0.6; selecting one particle with larger fitness from the two new child particles, and comparing the fitness value with the fitness values of the two parent particles generating the particle:
if the fitness value of the parent particle is large, replacing the parent particle, sequencing the atoms on each crossed particle from small to large according to the atom numbers, rearranging the respective speeds according to the indexes after the atoms on the particles are sequenced, and otherwise, not replacing;
s86, updating the historical optimal position and the global historical optimal position of the particles in the particles;
s87, judging whether the iteration stop condition of the particle swarm optimization is met, if so, executing the step S88, if not, returning to the step S82, and continuing to perform speed and position updating operation on the particles;
s88, taking the global historical optimal solution of the particle swarm as a reconstruction base of the image block;
s89, obtaining the optimal atomic combinations of all the image blocks, and calculating the estimated values x of all the image blocks by the following formulan：
xn＝Dn[(ΦDn)+yn]
Wherein D isnRepresents the optimal atomic combination of the image block, ynAn observation vector representing the image block, (-)+A pseudo-inverse of the matrix is calculated.
4. The non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering according to claim 3, wherein the step S81 specifically comprises:
s811, for each type of unidirectional image block, according to the overcomplete redundant dictionary ΨgInitializing a particle group with the size of 20, dividing the particle group into 5 groups, each group representing a direction, randomly initializing particles in each group, arranging atoms on each particle in order from small to large according to atom numbers, and randomly initializing the velocity of the particles to [ -L ]r,Lr]Any value of x 0.5, wherein LrThe size of a sub-dictionary corresponding to the direction r in the single-direction class overcomplete redundant dictionary belongs to {1, 2.., 36 };
s812, initializing a particle swarm with the scale of 36 for texture image blocks and multidirectional image blocks, wherein each particle represents two directions, one direction selects the direction which is the same as the particle number from a ridge wave overcomplete redundant dictionary, the other direction randomly selects one direction from the rest directions again, atoms on each particle are orderly arranged from small to large according to the original number, and then the speed of the particle is randomly initialized to [ -L ]m,Lm]Any value of x 0.5, wherein LmA size of an overcomplete ridge redundancy dictionary representing two selected representative directions, m representing a particle number, m being 1, 2.
S813, calculating the fitness value of each particle in the group of smooth image blocks, one-way image blocks, texture image blocks and multi-direction image blocks according to the following formula:
Figure FDA0002740690520000061
wherein, f (b)m) The fitness value Y of the m-th particle in the particle swarm of the image block corresponding to the multi-measurement matrix of the classiRepresenting image block X of class iiMultiple measurement vector observation matrix of, bmIs a solution represented by the m-th particle in the particle swarm, corresponding to a group of base atom combinations in the ridge overcomplete redundant dictionary, (. DEG)+A pseudo-inverse matrix representing a computational matrix,
Figure FDA0002740690520000071
represents the square of the matrix Frobenius norm;
s814, initializing a historical optimal solution and a global historical optimal solution of the particle swarm: and initializing the historical optimal solution of each particle in the particle swarm into the particle, obtaining the particle with the maximum fitness value in the whole particle swarm, and taking the particle as the global historical optimal solution.
5. The non-convex compressive sensing optimization reconstruction method based on sketch representation and structured clustering according to claim 3, wherein the step S82 specifically comprises:
s821, setting parameters in the particle swarm algorithm, and updating the particle velocity position of the particle swarm as follows:
Figure FDA0002740690520000072
wherein,
Figure FDA0002740690520000073
represents the t +1 th iterationThe updated speed corresponding to the u component of the m-th particle,
Figure FDA0002740690520000074
representing the velocity corresponding to the u component of the m-th particle in the current particle swarm,
Figure FDA0002740690520000075
representing the u-th component of the m-th particle in the current particle population,
Figure FDA0002740690520000076
the u-th component of the historical optimal position of the m-th particle in the current particle population,
Figure FDA0002740690520000077
represents the current global historical optimal position gtU is a positive integer, t denotes the current iteration, w denotes the inertial weight, c1Weight coefficient representing historical optimum value of particle tracking itself, c2Weight coefficient representing optimal value of particle tracking global history, and xi and eta are [0, 1]Two random numbers uniformly distributed in the interval;
s822, firstly, according to each current particle dimension component
Figure FDA0002740690520000078
R in the direction of the atom in (b), the atomic range [ g ] of the r-th direction is obtainedr,hr](ii) a Then, the direction constraint is carried out on the speed of the particles according to the following formula to obtain the controlled speed of the particles
Figure FDA0002740690520000079
Figure FDA00027406905200000710
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