CN105574824B - Multi-objective Genetic optimization compressed sensing image reconstructing method based on ridge ripple dictionary - Google Patents

Multi-objective Genetic optimization compressed sensing image reconstructing method based on ridge ripple dictionary Download PDF

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CN105574824B
CN105574824B CN201510939126.XA CN201510939126A CN105574824B CN 105574824 B CN105574824 B CN 105574824B CN 201510939126 A CN201510939126 A CN 201510939126A CN 105574824 B CN105574824 B CN 105574824B
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刘芳
李婷婷
李小青
郝红侠
焦李成
尚荣华
杨淑媛
马文萍
马晶晶
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Xidian University
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Abstract

The invention discloses a kind of multi-objective Genetic optimization compressed sensing image reconstructing method based on ridge ripple dictionary, mainly solves existing reconstructing method, leads to the problem of image reconstruction inaccuracy since degree of rarefication estimates inaccuracy, realization process is：1) differentiate picture block structure, by image block labeled as smooth, one direction and multi-direction；2) observation vector corresponding to different types of image block is clustered, and constructs initial population for every a kind of image block；3) intersection based on the variable-length encoding of different genes position, the insertion of new individual based on prior information and multiple spot mutation operation are executed to current population；4) the non-dominant disaggregation of current population is calculated, and calculates inflection point as optimal solution；5) estimated value that image block is calculated with optimal solution, is spliced into entire image in order.The present invention can find the degree of rarefication for being relatively suitble to image block, and find atom combination optimal under the degree of rarefication, and reconstruction quality is good, and robustness is high, can be used for the reconstruct of natural image and medical image.

Description

Multi-objective Genetic optimization compressed sensing image reconstructing method based on ridge ripple dictionary
Technical field
The invention belongs to technical field of image processing, are related to the non-convex compressed sensing image reconstructing method of multiple-objection optimization, It can be used for the reconstruct to medical image and natural image.
Background technique
Compressive sensing theory passes through the sparse characteristic of exploitation signal, in the item for being much smaller than Nyquist Nyquist sample rate Under part, stochastical sampling obtains the discrete sample of signal, then passes through non-linear algorithm for reconstructing ideally reconstruction signal.Compressed sensing It is theoretical it is critical that realize the combination of signal sampling and data compression, i.e., to signal sampling while also realize compression Purpose not only to save resource and bandwidth in this way to signal sampling far below Nyquist sample rate, but also alleviates higher band Width gives signal collecting device bring pressure.Under this new signal processing model, the frequency of sampling is no longer by signal bandwidth Size determined, but it is related to the factors such as the uncorrelated degree of observing matrix and sparse transformation base, the sparse degree of signal.
The non-convex compressed sensing image reconstruction algorithm based on ridge ripple dictionary learning proposed at present is calculated using genetic evolution Calligraphy learning obtains the combination of the more excellent atom on dictionary direction, is finally combined using the optimal atom and carrys out reconstructed image, but this Class algorithm requires that degree of rarefication is known in advance, that is, reconstructs the number of atom in the atom combinations of needs, but is actually answering In, degree of rarefication is often unknown.
Currently based in the non-convex compressed sensing image reconstruction algorithm of ridge ripple dictionary learning, degree of rarefication is usually fixed, also It is atom number required for one signal of fixed reconstruct, to ask optimal atom to combine, this is unreasonable, because one true Atom number, that is, degree of rarefication required for real signal reconstruction is often uncertain, thus exist due to degree of rarefication estimate it is inaccurate Really lead to the problem of image reconstruction inaccuracy.
Summary of the invention
It is an object of the invention to be directed to the deficiency of above-mentioned prior art, propose that a kind of multiple target based on ridge ripple dictionary is lost Optimization compressed sensing image reconstructing method is passed, to improve the image reconstruction accuracy under degree of rarefication unknown condition.
To achieve the above object, technical scheme is as follows：
(1) the Random Orthogonal Gauss observing matrix Φ and obtain to image block compression sampling every that sender sends are received One piece of observation y；
(2) image block corresponding to each observation vector y is tied according to the excessively complete dictionary of the ridge ripple organized by direction Structure differentiates, by image block labeled as smooth piece, one direction block and multi-direction piece, and records the direction of one direction block；
(3) to smooth piece, one direction block, multi-direction piece of corresponding measurement vector use respectively neighbour's propagation clustering AP algorithm into Row cluster；
(4) to the corresponding image block of every one kind observation vector, setting Population Size is N, if current evolutionary generation is I, if Each individual is set in population by the coding of two targets to forming, wherein the corresponding degree of rarefication for wanting reconstructed blocks of first aim, i.e., The number of atom in atom combination is reconstructed, second target correspondence wants the dictionary atom of reconstructed image block to combine, according to reconstructing The labeled classification of image block and the sub- dictionary of corresponding ridge ripple initialize population at individual, and calculate each individual in population Fitness value, obtain initial population；
(5) crossover operation based on the variable-length encoding of different genes position is executed to current population at individual, and updates corresponding kind The first aim of group's individual, the population after being intersected；
(6) insertion operation that new individual based on prior information is executed to the population after current intersect, obtains new population simultaneously Calculate the fitness value of new population individual；
(7) multiple spot mutation operation is executed to the second target of current new population individual；
(8) according to the first aim and corresponding fitness value of each individual of new population, non-dominant disaggregation F is calculated；
(9) uniform to select next-generation population at individual according to the number of new population individual in non-dominant disaggregation F；
(10) judge whether current population the number of iterations I reaches maximum number of iterations or reach fitness requirement, if Reach the number of iterations or fitness requirement then according to the non-dominant disaggregation F of population, the population at individual where inflection point is found, as most Then excellent individual executes step (11)；Otherwise the number of iterations increasing 1, i.e. I=I+1, return step (5)；
(11) according to the second target of optimum individual, the estimated value of all image blocks is calculated, and is combined by piecemeal sequence One complete image output.
Compared with prior art, the present invention having the following advantages that：
1. the present invention carries out the initialization of population according to direction and scale, so that population is begun looking for some preferably solutions Optimal solution provides a possibility that bigger to find optimal solution, decreases the time for finding optimal solution.
2. being encoded to degree of rarefication and atom combination in population together in the present invention, while by optimization, multiple target can be used Method find degree of rarefication and atom combination compromise optimal solution, improve the accuracy of reconstruct.
3. the present invention uses variable-length encoding to population, the crossover operation in random different crosspoints is carried out, so that generating more The solution of sample is conducive to the optimal solution for searching degree of rarefication compromise.
4. the present invention position radom insertion new individual sparse in degree of rarefication, this to increase the multifarious same of population When, it is more advantageous to and finds optimal solution, decrease the time for finding optimal solution.
Detailed description of the invention
Fig. 1 is implementation flow chart of the invention；
Fig. 2 is to use the present invention under 30% sample rate to the reconstruction result figure of Lena figure；
Fig. 3 is to use the present invention under 30% sample rate to the reconstruction result figure of Barbara figure.
Specific embodiment
Referring to Fig.1, implementation steps of the invention are as follows：
Step 1, the Random Orthogonal Gauss observing matrix Φ and obtain to image block compression sampling that sender sends are received Each piece of observation vector y.
Step 2, according to by direction tissue the excessively complete dictionary of ridge ripple, to image block corresponding to each observation vector y into Row structure discrimination by image block labeled as smooth piece, one direction block and multi-direction piece, and records the direction of one direction block.
(2a) calculates corresponding noise vector according to following formula, to the measurement vector y of each image block
In formula, y is the observation vector of image to be determined block, and Φ is Random Orthogonal Gauss observing matrix, and d is that a value is all 1 column vector, ()+It is the pseudo inverse matrix that matrix is calculated；
(2b) is to each noise vectorNoise figure ξ is calculated,WhereinSquare of two norm of vector；
(2c) judges whether ξ is less than threshold value 0.05, if it is less than just by the corresponding image block of the measurement labeled as smooth Block；Otherwise it does not just mark；
The image block that (2d) will not make marks is labeled as one direction block and multi-direction piece according still further to following steps：
The excessively complete dictionary of existing ridge ripple is divided into 36 sub- dictionary Ψ by direction by (2d1)1,Ψ2,...,Ψi,...Ψ36, To each observation vector y, it is reconstructed on this little dictionary with OMP algorithm respectively, each height is corresponded in the sequence of calculation Dictionary ΨiObservation residual error ri：
ri=| | y- Φ Dr[(ΦDr)+y] | |,
So obtain an observation residual sequence r1,r2,...,ri,...r36, find minimum value in sequence in the sequence Position i, i=1,2 ..., 36, in formula, y is the observation vector of image to be determined block, DrIt is sub- dictionary ΨiIn with y correlation most The combination of 10 big atoms, ()+It is the pseudo inverse matrix that matrix is calculated；
(2d2) using position i-2, i-1, i in sequence, i+1, i+2 find five corresponding residual values ri-2,ri-1,ri, ri+1,ri+2；If i is 1, ri-2And ri-1R is used respectively36And r35Instead of；If i is 2, ri-2Use r36Instead of；If i is 36, ri+1 And ri+2R is used respectively1And r2Instead of；If i is 35, ri+2Use r1Instead of；
The corresponding image block of observation vector y is marked in (2d3)：If ri-2Greater than ri-1, ri-1Greater than 1.2ri, ri+1Greatly In 1.2ri, and ri+2Greater than ri+1, then the corresponding image block of observation vector y is labeled as one direction, and i is appointed as the image The direction of block, otherwise just by the image block labeled as multi-direction.
Step 3, to smooth piece, one direction block, multi-direction piece of corresponding measurement vector uses neighbour's propagation clustering AP to calculate respectively Method is clustered.
There are many kinds of clustering methods, such as C means clustering method, fuzzy clustering method, affine clustering method, and neighbour propagates AP algorithm etc. is clustered, in the present embodiment, the clustering method used is neighbour's propagation clustering AP algorithm.Neighbour's propagation clustering AP is calculated Method, Affinity Propagation (AP) cluster are a kind of new clustering algorithms proposed on Science magazine for 2007. It is clustered according to the similarity between N number of data point, does not need to specify clusters number in advance.
It is implemented as follows：
(3a) clusters the corresponding observation vector of all smooth image blocks, obtains the cluster of smooth image block；
(3b) clusters the corresponding observation vector of all one direction image blocks, obtains the cluster of one direction image block；
(3c) clusters the corresponding observation vector of all multidirectional image blocks, obtains the cluster of multidirectional image block.
Step 4, to the corresponding image block of every one kind observation vector, according to the classification and correspondence for wanting reconstructed image block labeled Ridge ripple sub- dictionary population at individual is initialized, and calculate the fitness value of each individual in population, obtain initial population.
Population Size and degree of rarefication range is arranged in (4a)：For every a kind of smooth image block, setting Population Size N is 20, Degree of rarefication range is [3,50]；For every a kind of one direction image block, setting Population Size N is 20, degree of rarefication range be [10, 60]；For every a kind of multidirectional image block, setting Population Size N is 36, and degree of rarefication range is [10,60]；
(4b) initialization population P={ (s1,g1),(s2,g2),...,(sk,gk),...(sN,gN), k=1,2 ..., N, Wherein, skThe first aim of the corresponding each individual of population, gkThe second target of the corresponding each individual of population；
N number of positive integer { s is randomly generated in (4b1) within the scope of degree of rarefication1,s2,...,sk,...,sN, it is N number of just whole with this The first aim s of the number each individual of initialization populationk；
(4b2) is according to the first aim value s for planting each individualk, the second target g of each individual of initialization populationk：
For smooth piece, the atom of 5 scales before each direction in 36 directions of ridge ripple dictionary is taken out, by direction composition side It is random every time to take out s to sub- dictionarykA director dictionary, at random in this skS is taken out in a director dictionarykA atom composition is former Sub-portfolio, the second target g of initialization population individualk；
For one direction block, m-th of direction and 4 directions adjacent with m-th of direction or so are taken out from ridge ripple dictionary Sub- dictionary Ψ of the sub- dictionary as the one direction class image blockg, Ψg={ Ψm-2,Ψm-1,Ψm,Ψm+1,Ψm+2, wherein m The direction of the one direction class image block is indicated, at random in sub- dictionary ΨgMiddle taking-up skA atom composed atom combination, initialization kind The second target g of group's individualk；
For multi-direction class image block, the atom in 36 directions of ridge ripple dictionary is taken out by direction, forms direction dictionary Ψ1, Ψ2,...,Ψk,...Ψ36, to k-th of population at individual, s is found on k-th of director dictionary at randomkA atom composed atom Combination initializes the second target g of k-th of population at individualk；
(4d) calculates the fitness value of each individual by following fitness function to all individuals of initial population：
Wherein, f (gk) it is the suitable on k-th of population at individual of the corresponding image block of a kind of observation vector of certain to be reconstructed Angle value is answered, n is the measurement number for including in a kind of observation vector of certain to be reconstructed, and j is the number measured in certain one kind, j =1,2 ..., n, Y be cluster after certain one kind measurement vector, YjIt is j-th of survey in a kind of observation vector of certain to be reconstructed Measure vector, DjIt is the ridge ripple dictionary atom combination of j-th of image block of certain a kind of image block of reconstruct, AjBe to be reconstructed it is a certain The rarefaction representation coefficient of the corresponding image block of j-th of observation vector in the observation vector of class,It is square of two norm of vector.
Step 5, the crossover operation based on the variable-length encoding of different genes position is executed to current population at individual, and updated corresponding The first aim of population at individual, the population after being intersected.
Previous crossover operation, usually a selected integer is as crosspoint at random, then by the atom after crosspoint It is interchangeable, two new individuals for obtaining two execute different crosspoints as original individual lengths in this example Crossover operation obtains two and the different new individual of original individual lengths, is implemented as follows：
T is randomly selected to population at individual T=N × C according to crossover probability C in (5a), select every time a pair of of population at individual into Row intersects；
It is random to generate two positive integers for being less than selected population at individual first aim when (5b) intersects, as two Crosspoint；The atom behind the second target crosspoint of two population at individual is interchangeable again, wherein second target is original Sub-portfolio forms two new population at individual；
(5c) calculates the number of atom in two new population individual second targets, individual respectively as two new populations First aim；
(5d) is greater than the individual of the degree of rarefication upper range limit of setting to the first aim of new population individual, by degree of rarefication model The upper bound enclosed is as its first aim, according still further to the direction of atom in second target, select atom combination as it Second target；
(5d1) counts the direction of atom in individual second target first；
(5d2) respectively selects an atom from first in each direction；
Whether the atom number that (5d3) judgement is selected reaches requirement, stops if reaching requirement, otherwise continues (5d2) Step, the atom finally selected combine the second target as new individual.
Step 6, the insertion operation that new individual based on prior information is executed to the population after current intersect, obtains new population And calculate the fitness value of new population individual.
It is empty set that new degree of rarefication value set E, which is arranged, in (6a) first, and the first aim for taking out all population at individual saves Into set G；
(6b) arranges all elements in G from small to large, calculates the spacing value between two adjacent elements；
(6c) judges to be greater than 2 either with or without the spacing value between two adjacent elements, if there is just therefrom selecting spacing value most Two big elements, the median for calculating the two elements is added in new degree of rarefication set E, and the value is also added Into original degree of rarefication value set G；
(6d) continues step (6b) until there are two spacing values between neighbouring degree of rarefication to be greater than 2.
(6e) by the value in new degree of rarefication set E, as the first aim of new insertion population at individual, then further according to The labeled classification of image block selects the combination of atom composed atom as their second mesh from corresponding sub- dictionary at random Mark；
If what the image block to be reconstructed was labeled is smooth piece, 5 before taking out all directions in entire ridge ripple dictionary The atom of a scale forms a scale dictionary, selects integer corresponding to individual first aim at random in scale dictionary The combination of atom composed atom, the second target as individual；
If the image block to be reconstructed it is labeled be one direction block, selected at random from corresponding director dictionary The combination of integer atom composed atom corresponding to body first aim, the second target as individual；
If the image block to be reconstructed it is labeled be multi-direction piece, select individual the at random from entire ridge ripple dictionary The combination of integer atom composed atom corresponding to one target, the second target as individual；
(6d) calculates the fitness value of each new population individual according to the second target of new population individual.
Step 7, multiple spot mutation operation is executed to the second target of current population at individual.
(7a) is according to B population at individual B=N × C ' of mutation probability C ' random selection；
When (7b) makes a variation, for the second target of each selected population at individual, i.e., any position in atom combination The atom set is replaced with the atom picked out at random in ridge ripple dictionary, generates a new population at individual；
(7c) calculates the fitness for the new population individual that variation generates；
(7d) compares the fitness of parent and filial generation, if the fitness of filial generation is less than parent, just replaces parent with filial generation, Otherwise it does not replace.
Step 8, according to the first aim and corresponding fitness value of each individual of new population, non-dominant disaggregation F is calculated.
(8a) sets non-domination solution F as empty set, and domination disaggregation D is empty set；
(8b) is to each population at individual pt, t=1,2 ..., N find the population at individual that first aim is less than it, remember It records in set H；
(8c) compares population at individual ptWith the fitness value of population at individual in set H, if there are a populations in set H Individual ph, h=1,2 ..., N, h ≠ t, its fitness is less than ptFitness, then population at individual ptBy population at individual phIt is propped up Match, i.e., by population at individual ptIt is added to and dominates in disaggregation Q；Otherwise, ptIt is not dominated by any individual, adds it in non-branch With in solution F；
(8d) judges each individual in population according to this, finally obtains non-domination solution F and dominates disaggregation Q.
Step 9, uniform to select next-generation population at individual according to the number of population at individual in non-dominant disaggregation F.
If the number of population at individual is just equal to Population Size in non-dominant disaggregation F, non-dominant disaggregation F is directly selected In population at individual as next-generation population；
If the number of population at individual is less than Population Size in non-dominant disaggregation F, all non-dominant disaggregation F are first selected In population at individual, then from dominate disaggregation Q in select remaining population at individual, obtain next-generation population；
If the number of population at individual is greater than Population Size in non-dominant disaggregation F, according to following in non-dominant disaggregation F Step, selected population individual enter next-generation population：
The first step：By the smallest population at individual p of first aim in non-dominant disaggregation FaIt is maximum with first aim Population at individual pbIt is added to next-generation populationIn, and v=2 is set, v is next-generation populationThe sum of middle population at individual, w reduce 2, w be the population at individual sum in non-dominant disaggregation F；
Second step：Remaining population at individual is calculated in non-dominant disaggregation F to populationThe minimum euclidean distance b of middle individual1, b2,...,be,...,bw-v, e=1,2 ..., w-v；
Third step：In Euclidean distance b1,b2,...,be,...,bw-vPopulation at individual p corresponding to middle maximizingc, will It is added to next-generation populationIn, v increases by 1, i.e. v=v+1；W reduces 1, i.e. w=w-1；
4th step：Judgement is added to next-generation populationWhether the sum of middle individual reaches requirement, stops if reaching requirement Only, otherwise continue second step.
Step 10, according to the non-dominant disaggregation F of population, the population at individual where inflection point is found.
(10a) establishes one according to the first aim and second target of each population at individual in non-dominant disaggregation F Two-dimensional coordinate system：The first aim of population at individual is as abscissa；Fitness corresponding to the second target of population at individual Value is used as ordinate；
(10b) finds the smallest population at individual p of first aimaWith the maximum population at individual p of first aimb；
(10c) is calculated in addition to population at individual paAnd pbAll population at individual in addition are to paAnd pbThe distance of line, then distance Population at individual corresponding to maximum is exactly the population at individual of inflection point position.
Step 11, judge whether current population the number of iterations I reaches maximum number of iterations or reach fitness requirement, such as Fruit reaches the number of iterations or fitness requirement then retains second target execution step (12) of optimum individual；Otherwise the number of iterations Increasing 1, i.e. I=I+1, return step (5).
Step 12, according to the second target of optimum individual, the estimated value of all image blocks is calculated, and presses piecemeal sequence and spells At a complete image output.
(12a) calculates the estimated value of all image blocks by following formula:
Wherein, j is the number measured in certain one kind, j=1,2 ..., n, xjIndicate j-th of image of certain a kind of image block The estimated value of block,Expression wants the optimal atom of reconstructed image block to combine, YjIndicate j-th of observation in certain a kind of observation vector Vector, ()+Indicate the pseudo inverse matrix of calculating matrix.
Effect of the invention is further illustrated by the image and data of following emulation：
1. simulated conditions
(1) emulation experiment uses Lena figure, Barbara figure in 512 × 512 standard testing image library, image Block size is set to 16 × 16；
(2) observing matrix of this experiment is random Gaussian observing matrix, sample rate 30%；
(3) the Ridgelet redundant dictionary scale that this experiment uses is 12032, altogether 36 directions；
(4) the smooth class of this experiment, the number of iterations 100 times each, one direction class iteration 50 times when multi-direction class reconstructs；
(5) this experimental selection CPU is Inter i5-3470, dominant frequency 3.2GHZ, inside saves as 4G, and operating system is 64 Win7, emulation platform Matlab2012a.
2. emulation content and result
Emulation 1 is reconstructed Lena figure with the method for the present invention, simulation result is such as under conditions of sample rate is 30% Shown in Fig. 2, wherein：
Fig. 2's the experiment results show that the reconstructed image obtained using the method for the present invention
Fig. 2 (a) is Lena original image, and Fig. 2 (b) is the partial enlarged view of Fig. 2 (a)；
Fig. 2 (c) is the reconstruct image obtained with the present invention, and Fig. 2 (d) is the partial enlarged view of Fig. 2 (c)；
Fig. 2's the experiment results show that the reconstructed image obtained using the method for the present invention, image is smoother, from each part As can be seen that the smooth part that the present invention goes out lena arm reconstructs very smooth, edge is apparent again, is said for the comparison of enlarged drawing The bright present invention has found the suitable degree of rarefication of reconstructed image block, more preferable with this degree of rarefication quality reconstruction.
Emulation 2 is reconstructed Barbara figure with the method for the present invention, simulation result under conditions of sample rate is 30% As shown in figure 3, wherein：
Fig. 3 (a) is Barbara original image, and Fig. 3 (b) is the partial enlarged view of Fig. 3 (a)；
Fig. 3 (c) is the reconstruct image obtained with the present invention, and Fig. 3 (d) is the partial enlarged view of Fig. 3 (c)；
Fig. 3's the experiment results show that the reconstructed image obtained using the method for the present invention, reconstructs Barbara smooth part Must be very smooth, Edge texture is clear, illustrates that the present invention has found the suitable degree of rarefication of reconstructed image block, is reconstructed and is imitated with this degree of rarefication Fruit is more preferable.
In conclusion the present invention is realized by regarding degree of rarefication and atom combination as two targets while optimizing, obtain The suitable degree of rarefication of reconstructed image and the combination of optimal atom, obtain to the good compressed sensing quality reconstruction of natural image.

Claims (10)

1. a kind of multi-objective Genetic optimization compressed sensing image reconstructing method based on ridge ripple dictionary, it is characterized in that：Including as follows Step：
(1) the Random Orthogonal Gauss observing matrix Φ that sender sends and each piece obtained to image block compression sampling are received Observation vector y；
(2) structure is carried out to image block corresponding to each observation vector y according to the excessively complete dictionary of the ridge ripple organized by direction to sentence Not, by image block labeled as smooth piece, one direction block and multi-direction piece, and the direction of one direction block is recorded：
(3) to smooth piece, one direction block, multi-direction piece of corresponding observation vector is gathered with neighbour's propagation clustering AP algorithm respectively Class；
(4) to the corresponding image block of every one kind observation vector, setting Population Size is N, if current evolutionary generation is I, setting kind Each individual is by the coding of two targets to forming in group, and wherein the corresponding degree of rarefication for wanting reconstructed blocks of first aim, that is, reconstruct The number of atom in atom combination, second target correspondence wants the dictionary atom of reconstructed image block to combine, according to wanting reconstructed image The labeled classification of block and the sub- dictionary of corresponding ridge ripple initialize population at individual, and calculate each individual in population fit Angle value is answered, initial population is obtained；
(5) crossover operation based on the variable-length encoding of different genes position is executed to current population at individual, and updates corresponding population The first aim of body, the population after being intersected；
(6) insertion operation that new individual based on prior information is executed to the population after current intersect, obtains new population and calculates The fitness value of new population individual；
(7) multiple spot mutation operation is executed to the second target of current new population individual；
(8) according to the first aim and corresponding fitness value of each individual of new population, non-dominant disaggregation F is calculated；
(9) uniform to select next-generation population at individual according to the number of new population individual in non-dominant disaggregation F；
(10) judge whether current population the number of iterations I reaches maximum number of iterations or reach fitness requirement, if reached The number of iterations or fitness require to find the population at individual where inflection point then according to the non-dominant disaggregation F of population, as optimal Then body executes step (11)；Otherwise the number of iterations increasing 1, i.e. I=I+1, return step (5)；
(11) according to the second target of optimum individual, the estimated value of all image blocks is calculated, and is combined into one by piecemeal sequence Complete image output.
2. the multi-objective Genetic optimization compressed sensing image reconstructing method according to claim 1 based on ridge ripple dictionary, Structure is carried out to image block corresponding to each observation vector according to the excessively complete dictionary of ridge ripple organized by direction in middle step (2) Differentiate, by image block labeled as smooth piece, one direction block and multi-direction piece, and record the direction of one direction block, according to following step It is rapid to carry out：
(2a) calculates corresponding noise vector to the observation vector y of each image block first according to following formula
In formula, y is the observation vector of image to be determined block, and Φ is Random Orthogonal Gauss observing matrix, and d is that a value is all 1 column Vector, ()+It is the pseudo inverse matrix that matrix is calculated；
(2b) is to each noise vectorNoise figure ξ is calculated,WhereinSquare of two norm of vector；
(2c) judges whether ξ is less than threshold value 0.05, if it is less than just by the corresponding image block of observation vector y labeled as smooth Block；Otherwise it does not just mark；
The image block that (2d) will not make marks is labeled as one direction block and multi-direction piece according still further to following steps：
The excessively complete dictionary of existing ridge ripple is divided into 36 sub- dictionary Ψ by direction by (2d1)1,Ψ2,...,Ψi,...Ψ36, to every One observation vector y is reconstructed on this little dictionary with OMP algorithm respectively, and each sub- dictionary is corresponded in the sequence of calculation ΨiObservation residual error ri：
ri=| | y- Φ Dr[(ΦDr)+Y] | |,
So obtain an observation residual sequence r1,r2,...,ri,...r36, find the position of minimum value in the sequence in sequence I, i=1,2 ..., 36, in formula, y is the observation vector of image to be determined block, DrIt is sub- dictionary ΨiIn with y correlation maximum The combination of 10 atoms, ()+It is the pseudo inverse matrix that matrix is calculated；
(2d2) using position i-2, i-1, i in sequence, i+1, i+2 find five corresponding residual values ri-2,ri-1,ri,ri+1, ri+2；If i is 1, ri-2And ri-1R is used respectively36And r35Instead of；If i is 2, ri-2Use r36Instead of；If i is 36, ri+1With ri+2R is used respectively1And r2Instead of；If i is 35, ri+2Use r1Instead of；
The corresponding image block of observation vector y is marked in (2d3)：If ri-2Greater than ri-1, ri-1Greater than 1.2ri, ri+1It is greater than 1.2ri, and ri+2Greater than ri+1, then the corresponding image block of observation vector y is labeled as one direction, and i is appointed as the image block Direction, otherwise just by the image block labeled as multi-direction.
3. the multi-objective Genetic optimization compressed sensing image reconstructing method according to claim 1 based on ridge ripple dictionary, According to the classification and the sub- dictionary of corresponding ridge ripple for wanting reconstructed image block labeled in middle step (4), population at individual is carried out initial Change, and calculate the fitness value of each individual in population, carries out in accordance with the following steps：
Population Size and degree of rarefication range is arranged in (4a)：For every a kind of smooth image block, setting Population Size N is 20, sparse Spending range is [3,50]；For every a kind of one direction image block, setting Population Size N is 20, and degree of rarefication range is [10,60]； For every a kind of multidirectional image block, setting Population Size N is 36, and degree of rarefication range is [10,60]；
(4b) initialization population P={ (s1,g1),(s2,g2),...,(sk,gk),...(sN,gN), k=1,2 ..., N, wherein skThe first aim of the corresponding each individual of population, gkThe second target of the corresponding each individual of population；
N number of positive integer { s is randomly generated in (4b1) within the scope of degree of rarefication1,s2,...,sk,...,sN, it is initial with this N number of positive integer Change the first aim s of each individual of populationk；
(4b2) is according to the first aim value s for planting each individualk, the second target g of each individual of initialization populationk：
For smooth piece, the atom of 5 scales before each direction in 36 directions of ridge ripple dictionary is taken out, forms director by direction Dictionary, it is random every time to take out skA director dictionary, at random in this skS is taken out in a director dictionarykA atom composed atom group It closes, the second target g of initialization population individualk；
For one direction block, the son in m-th of direction and 4 direction adjacent with m-th of direction or so is taken out from ridge ripple dictionary Sub- dictionary Ψ of the dictionary as the one direction class image blockg, Ψg={ Ψm-2,Ψm-1,Ψm,Ψm+1,Ψm+2, wherein m is indicated The direction of the one direction class image block, at random in sub- dictionary ΨgMiddle taking-up skA atom composed atom combination, initialization population The second target g of bodyk；
For multi-direction class image block, the atom in 36 directions of ridge ripple dictionary is taken out by direction, forms direction dictionary Ψ1, Ψ2,...,Ψk,...Ψ36, to k-th of population at individual, s is found on k-th of director dictionary at randomkA atom composed atom Combination initializes the second target g of k-th of population at individualk；
(4d) calculates the fitness value of each individual by following fitness function to all individuals of initial population：
Wherein, f (gk) be the corresponding image block of a kind of observation vector of certain to be reconstructed the fitness on k-th of population at individual Value, n are the numbers comprising observation vector in a kind of observation vector of certain to be reconstructed, and j is the number of observation vector in certain one kind, J=1,2 ..., n, YjIt is j-th of observation vector in a kind of observation vector of certain to be reconstructed, DjIt is certain a kind of image of reconstruct The ridge ripple dictionary atom of j-th of image block of block combines, AjIt is j-th of observation vector in a kind of observation vector of certain to be reconstructed The rarefaction representation coefficient of corresponding image block,It is square of two norm of vector.
4. the multi-objective Genetic optimization compressed sensing image reconstructing method according to claim 1 based on ridge ripple dictionary, The crossover operation based on the variable-length encoding of different genes position is executed to current population at individual in middle step (5), and updates corresponding kind The first aim of group's individual, carries out in accordance with the following steps：
T is randomly selected to population at individual T=N × C according to crossover probability C in (5a), and a pair of of population at individual is selected to be handed over every time Fork；
It is random to generate two positive integers for being less than selected population at individual first aim when (5b) intersects, intersect as two Point；The atom behind the second target crosspoint of two population at individual is interchangeable again, wherein second target is atom group It closes, forms two new population at individual；
(5c) calculates the number of atom in two new population individual second targets, respectively as the first of two new population individuals A target；
(5d) is greater than the individual of the degree of rarefication upper range limit of setting to the first aim of new population individual, by degree of rarefication range The upper bound selects atom combination as its second as its first aim according still further to the direction of atom in second target A target；
(5d1) counts the direction of atom in individual second target first；
(5d2) respectively selects an atom from first in each direction；
Whether the atom number that (5d3) judgement is selected reaches requirement, stops if reaching requirement, otherwise continues (5d2) step, The atom finally selected combines the second target as new individual.
5. the multi-objective Genetic optimization compressed sensing image reconstructing method according to claim 1 based on ridge ripple dictionary, The insertion operation of new individual based on prior information is executed in middle step (6) to current population, then calculates the suitable of new population individual Angle value is answered, is carried out in accordance with the following steps：
(6a) be arranged first new degree of rarefication value set E be empty set, take out all population at individual first aim be saved in it is dilute It dredges in angle value set G；
(6b) arranges all elements in G from small to large, calculates the spacing value between two adjacent elements；
(6c) judges either with or without the spacing value between two adjacent elements greater than 2, maximum if there is just therefrom selecting spacing value Two elements, the median for calculating the two elements is added in new degree of rarefication set E, and the value is also added to original In some degree of rarefication value set G；
(6d) continues step (6b) until there are two spacing values between neighbouring degree of rarefication to be greater than 2；
(6e) by the value in new degree of rarefication set E, as the first aim of new insertion population at individual, then further according to image The labeled classification of block selects the combination of atom composed atom as their second target from corresponding sub- dictionary at random；
If what the image block to be reconstructed was labeled is smooth piece, 5 rulers before taking out all directions in entire ridge ripple dictionary The atom of degree forms a scale dictionary, selects integer atom corresponding to individual first aim at random in scale dictionary Composed atom combination, the second target as individual；
If the image block to be reconstructed it is labeled be one direction block, select individual the at random from corresponding director dictionary The combination of integer atom composed atom corresponding to one target, the second target as individual；
If what the image block to be reconstructed was labeled is multi-direction piece, individual first is selected at random from entire ridge ripple dictionary The combination of integer atom composed atom corresponding to target, the second target as individual；
(6d) calculates the fitness value of each new population individual according to the second target of new population individual.
6. the multi-objective Genetic optimization compressed sensing image reconstructing method according to claim 1 based on ridge ripple dictionary, Multiple spot mutation operation is executed to the second target of current population at individual in middle step (7), is carried out in accordance with the following steps：
(7a) is according to B population at individual B=N × C ' of mutation probability C ' random selection；
When (7b) makes a variation, for the second target of each selected population at individual, i.e., any a position in atom combination Atom is replaced with the atom picked out at random in ridge ripple dictionary, generates a new population at individual；
(7c) calculates the fitness for the new population individual that variation generates；
(7d) compares the fitness of parent and filial generation, if the fitness of filial generation is less than parent, just replaces parent with filial generation, otherwise It does not replace.
7. the multi-objective Genetic optimization compressed sensing image reconstructing method according to claim 1 based on ridge ripple dictionary, Non-domination solution collection F is calculated in middle step (8), is carried out in accordance with the following steps：
(8a) sets non-domination solution F as empty set, and domination disaggregation Q is empty set；
(8b) is to each population at individual pt, t=1,2 ..., N find the population at individual that first aim is less than it, are recorded In set H；
(8c) compares population at individual ptWith the fitness value of population at individual in set H, if there are a population at individual in set H ph, h=1,2 ..., N, h ≠ t, its fitness is less than ptFitness, then population at individual ptBy population at individual phIt is dominated, I.e. by population at individual ptIt is added to and dominates in disaggregation Q；Otherwise, ptIt is not dominated by any individual, adds it in non-domination solution In F；
(8c) judges each individual in population according to this, finally obtains non-domination solution F and dominates disaggregation Q.
8. the multi-objective Genetic optimization compressed sensing image reconstructing method according to claim 1 based on ridge ripple dictionary, It is uniform to select next-generation new population individual according to the number of population at individual in non-dominant disaggregation F in middle step (9), it is basis The number of population at individual and Population Size carry out in more non-dominant disaggregation F：
If the number of population at individual is just equal to Population Size in non-dominant disaggregation F, directly select in non-dominant disaggregation F Population at individual is as next-generation population；
If the number of population at individual is less than Population Size in non-dominant disaggregation F, first select in all non-dominant disaggregation F Population at individual, then remaining population at individual is selected from dominating in disaggregation Q, obtain next-generation population；
If the number of population at individual is greater than Population Size in non-dominant disaggregation F, according to following step in non-dominant disaggregation F Suddenly, selected population individual enters next-generation population：
The first step：By the smallest population at individual p of first aim in non-dominant disaggregation FaWith first aim maximum population Body pbIt is added to next-generation populationIn, and v=2 is set, v is next-generation populationThe sum of middle population at individual, w reduce 2, w right and wrong Dominate the population at individual sum in disaggregation F；
Second step：Remaining population at individual is calculated in non-dominant disaggregation F to populationThe minimum euclidean distance b of middle individual1, b2,...,be,...,bw-v, e=1,2 ..., w-v；
Third step：In Euclidean distance b1,b2,...,be,...,bw-vPopulation at individual p corresponding to middle maximizingc, by itself plus Enter to next-generation populationIn, v increases by 1, i.e. v=v+1；W reduces 1, i.e. w=w-1；
4th step：Judgement is added to next-generation populationWhether the sum of middle individual reaches requirement, stops if reaching requirement, Otherwise continue second step.
9. the multi-objective Genetic optimization compressed sensing image reconstructing method according to claim 1 based on ridge ripple dictionary, According to the non-dominant disaggregation F of population in middle step (10), the population at individual where inflection point is found, is carried out in accordance with the following steps：
(10a) establishes a two dimension according to the first aim and second target of each population at individual in non-dominant disaggregation F Coordinate system：The first aim of population at individual is as abscissa；Fitness value corresponding to the second target of population at individual is made For ordinate；
(10b) finds the smallest population at individual p of first aimaWith the maximum population at individual p of first aimb；
(10c) is calculated in addition to population at individual paAnd pbAll population at individual in addition are to paAnd pbThe distance of line, then distance is maximum Corresponding population at individual is exactly the population at individual of inflection point position.
10. the multi-objective Genetic optimization compressed sensing image reconstructing method according to claim 1 based on ridge ripple dictionary, According to the second target of optimum individual described in middle step (11), the estimated value of all image blocks is calculated, according to following formula It carries out：
Wherein, AjIt is the rarefaction representation system of the corresponding image block of j-th of observation vector in a kind of observation vector of certain to be reconstructed Number, j is the number of observation vector in certain one kind, j=1,2 ..., n, XjIndicate estimating for j-th of image block of certain a kind of image block Evaluation,Expression wants the optimal atom of reconstructed image block to combine, YjIndicate j-th of observation vector in certain a kind of observation vector, (·)+Indicate the pseudo inverse matrix of calculating matrix.
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