CN104881846A - Structured image compressive sensing restoration method based on double-density dual-tree complex wavelet - Google Patents

Abstract

The invention provides a structured image compressive sensing restoration method based on double-density dual-tree complex wavelets. The structured image compressive sensing restoration method combines a structured sparse model with a CoSaMP (Compressive Sampling Matching Pursuit) algorithm, integrates a coefficient structural model based on double-density dual-tree complex wavelet transform therein, and further enhances the reconstruction performance. The method provided by the invention can obtain higher image reconstruction quality by utilizing the structured sparse model of images under wavelet transform and adopting the double-density dual-tree complex wavelet transform for solving defects of the wavelet transform.

Description

Based on the structured image compressed sensing method of reducing of dual density dual-tree complex wavelet

Technical field

The present invention relates to digital picture and signal transacting field, particularly relate to a kind of structured image compressed sensing method of reducing and system.

Background technology

Compressive sensing theory is by utilizing the sparse characteristic of signal, and under the condition much smaller than Nyquist sampling rate, stochastic sampling obtains the discrete sample of signal, then by nonlinear algorithm reconstruction signal.If its core concept is signal is sparse on certain transform-based Ψ, coding side with one with Ψ incoherent calculation matrix Φ signal is projected to a lower dimensional space, decoding end by solve optimization problem can from less is more Accurate Reconstruction original signal.

Restructing algorithm, as the key link in compressive sensing theory, receives much concern always.In recent years, propose multiple restructing algorithm: base back tracking method (Basis Pursuit, BP), interior point method (Inner Point, IP), gradient projection method (Gradient Projection Algorithm, GPA), iteration method (Iteration Threshold, IT); Matching pursuit algorithm (Matching Pursuit, MP), orthogonal matching pursuit method (Orthogonal Matching Pursuit, OMP), regularization orthogonal matching pursuit method (Regularization Orthogonal Matching Pursuit, ROMP), subspace back tracking method (Subspace Pursuit, SP), compression sampling match tracing (Compressive Sampling Matching Pursuit, CoSaMP) etc.

The CS restructing algorithm of these standards only utilizes signal and the image sparse prior information under wavelet transformation, and the structure distribution feature not utilizing conversion coefficient to have, in order to accurately original signal can be rebuild, for the tree construction after image wavelet transform, the people such as Baraniuk propose the modeling method based on wavelet tree structure, but the defect due to wavelet transformation: (1), to data sensitive, (2) directivity is poor, and (3) do not have spatial information.For this reason, within 1999, Kingsbury proposes dual-tree complex wavelet transform (Dual-tree Complex Wavelet Transform, DT-CWT), this algorithm can wavelet transform (Discrete Wavelet Transform, DWT) information provided describes direction to be brought up to ± and 15 °, 6 directions of ± 45 ° and ± 75 °.However, still there is the limitation of directivity deficiency.

Summary of the invention

In order to solve the problems of the prior art, the invention provides a kind of structured image compressed sensing method of reducing based on dual density dual-tree complex wavelet, higher image reconstruction quality can be obtained.。

The present invention is achieved through the following technical solutions:

Based on a structured image compressed sensing method of reducing for dual density dual-tree complex wavelet, comprise the steps:

Compressed encoding step: to being of a size of N ₁× N ₂two dimensional image be launched into N=N by row ₁× N ₂one-dimensional vector x, the linear compression y=Φ based on compressed sensing is carried out to one-dimensional vector x _x, obtain corresponding compression result y, and y and Φ be transferred to decoder module;

Decoding step: utilize dual density dual-tree complex wavelet transform as sparse base Ψ, the factor alpha of image under wavelet transformation presents the priori conditions of tree structured feature, decodes in conjunction with CoSaMP algorithm, is below decoding step:

A. extract the high fdrequency component in 16 directions of dual density dual-tree complex wavelet transform, form 16 wavelet basis Ψ _i, i=1 ~ 16, Jacobian matrix Θ _i=Φ Ψ _i;

B. initiation parameter α ₀=0, signal residual error r ₀=y, signal support set l=1, K are signal degree of rarefication;

C. signal agency is calculated pruning residue according to wavelet tree structure estimates as the new support set Γ=supp (M (c, K)) added, and merges support set Ω=Γ ∪ supp (α _l-1), calculate Signal estimation value ${\left(s\right)}_{\mathrm{\Ω}}={\left({\mathrm{\Θ}}_{\mathrm{i\Ω}}^T{\mathrm{\Θ}}_{\mathrm{i\Ω}}\right)}^{-1}{\mathrm{\Θ}}_{\mathrm{i\Ω}}^{T}y;$

D. according to wavelet tree structure shear signal alpha _l=M (s, K), Optimization of Wavelet tree construction $M(\mathrm{\α},K)=\arg min||\mathrm{\α}-\stackrel{-}{\mathrm{\α}}||,\stackrel{-}{\mathrm{\α}}\∈M_K,$ Upgrade residual error r _l=y-Θ _iα _lif meet stopping criterion for iteration, circulate end, obtains otherwise make l=l+1, return step c, obtained by 16 directions recovering signal is obtained through dual density dual-tree complex wavelet inverse transformation

As a further improvement on the present invention, in described decoding step, by the compression result y got and calculation matrix Φ, by solving obtain again by obtain recovering signal through inverse wavelet transform, complete reconstruct; Wherein y is the compression result that M × 1 is tieed up, y=Φ x, Θ _i=Φ Ψ _ithe matrix of to be size be M × N, be coefficient to be estimated, solve this Optimum Solution after, original signal x reconstructs estimated value and is for N × 1 dimensional signal, then will n is reduced to by row ₁× N ₂picture signal.

As a further improvement on the present invention, in described step a, utilize dual density dual-tree complex wavelet transform as sparse base Ψ, dual density dual-tree complex wavelet transform to be a kind of redundance be 3 tight frame conversion, its bank of filters is made up of two different dual density wavelet filter groups, during signal decomposition, two bank of filters process signal simultaneously, exchanges data is not had between two branches, reconstruction filter banks is made up of the backward of analysis filter bank, " dual density " means that each branching filter group is made up of a scaling function and two wavelet functions respectively, the increase of filtering channel improves design freedom, two dimension dual density dual-tree complex wavelet describes the information of 16 principal directions, and each principal direction has two small echos, respectively as real part and the imaginary part of 16 complex scalar wavelet, more accurate to the feature interpretation of image.

As a further improvement on the present invention, in described step c: prune residue according to wavelet tree structure and estimate as the new support set Γ=supp (M (c added, K)), the coefficient of picture signal after wavelet transformation can form a tree construction naturally, and maximum wavelet coefficient can along branch's cluster of wavelet tree, one that material is thus formed wavelet coefficient is communicated with tree-model, and it can perform well in compressed sensing restructing algorithm; Wherein, M is compression categorizing selection algorithm, be used for calculating Best tree to be similar to, first calculate in tree with the absolute value of each subtree wavelet coefficient mean value of each node root, using the energy of the maximal value in absolute value as this node, the node claiming this energy maximum is supernode, and retains whole coefficients of subtree corresponding to supernode, optimum subtree set is just made up of these coefficients, thus realizes the thought of tree construction optimum.

As a further improvement on the present invention, in described steps d: according to wavelet tree structure shear signal alpha _l=M (s, K), Optimization of Wavelet tree construction the coefficient of picture signal after wavelet transformation can form a tree construction naturally, and maximum wavelet coefficient can along branch's cluster of wavelet tree, one that material is thus formed wavelet coefficient is communicated with tree-model, and it can perform well in compressed sensing restructing algorithm; Wherein, M is compression categorizing selection algorithm, be used for calculating Best tree to be similar to, first calculate in tree with the absolute value of each subtree wavelet coefficient mean value of each node root, using the energy of the maximal value in absolute value as this node, the node claiming this energy maximum is supernode, and retains whole coefficients of subtree corresponding to supernode, optimum subtree set is just made up of these coefficients, thus realizes the thought of tree construction optimum.

As a further improvement on the present invention, M algorithm comprises the steps:

(1). input B >=0, γ >=0, wherein B is that input data set closes, and γ is iterations, namely chooses at most γ node in tree construction;

(2). initialization v (k) :=B (k), is namely expressed as v (k), n (k) the coefficient value of a kth node :=1, chooses 1 node, suppose that the node chosen at first is not for needing the node chosen, Γ :=0, Γ is loop iteration, suppose that the node chosen at first exists father node, p (k) represents the father node of a kth node;

(3). circulation starts, and finds namely the supernode S finding coefficient value maximum in all supernode S ^*;

(4) if. if i.e. this supernode S ^*father node p (S ^*) be the node that will look for, then arrange Γ :=Γ+n (S ^*), namely obtain according to formula wherein n (S ^*) nodes that comprises for this supernode, otherwise, by S ^*with p (S ^*) merge into 1 new supernode S wherein, v (S)=(v (S ₁) n (S ₁)+v (S ₂) n (S ₂))/(n (S ₁)+n (S ₂)), n (S)=n (S ₁)+n (S ₂), terminate to select, end loop, Output rusults node time, namely the node needed is obtained, supernode S is that node k and its father node p (k) merge the general node formed, and the coefficient value of supernode is defined as v (S)=(B (k)+B [P (k)])/2.

Present invention also offers a kind of structured image compressed sensing restoring system based on dual density dual-tree complex wavelet, comprise compressed encoding module and decoder module; Described system performs the structured image compressed sensing method of reducing based on dual density dual-tree complex wavelet of the present invention.

The invention has the beneficial effects as follows: method and system of the present invention, due to the structural sparse model that utilizes image and have under wavelet transformation and for the defect of wavelet transformation and the dual density dual-tree complex wavelet transform adopted, can obtain higher image reconstruction quality.The method and system that the present invention proposes all have certain advantage compared with classic method from objective evaluation index or subjective vision effect.

Accompanying drawing explanation

Fig. 1 is the structured image compressed sensing method of reducing schematic diagram based on dual density dual-tree complex wavelet of the present invention;

Fig. 2 is one dimension dual density dual-tree complex wavelet transform schematic diagram of the present invention;

Fig. 3 is the directional diagram of two-dimentional dual density dual-tree complex wavelet transform of the present invention;

Fig. 4 is wavelet tree structural model schematic diagram;

Fig. 5 is " Lena " of the present invention figure reconstruction property simulation comparison figure;

Fig. 6 is " Lena " of the present invention reconstructed image.

Embodiment

The invention discloses a kind of structured image compressed sensing method of reducing based on dual density dual-tree complex wavelet, as shown in Figure 1, comprise the steps:

Compressed encoding step: to being of a size of N ₁× N ₂two dimensional image be launched into N=N by row ₁× N ₂one-dimensional vector x, the linear compression y=Φ x based on compressed sensing is carried out to one-dimensional vector x, obtains corresponding compression result y, and y and Φ is transferred to decoding end;

Decoding step: utilize dual density dual-tree complex wavelet transform as sparse base Ψ, the factor alpha of image under wavelet transformation presents the priori conditions of tree structured feature, decodes in conjunction with CoSaMP (Compressive Sampling Matching Pursuit) algorithm.The concrete steps of decoding are:

A. extract the high fdrequency component in 16 directions of dual density dual-tree complex wavelet transform, form 16 wavelet basis Ψ _i, i=1 ~ 16, Jacobian matrix Θ _i=Φ Ψ _i;

B. initiation parameter α ₀=0, signal residual error r ₀=y, signal support set l=1, K are signal degree of rarefication;

C. signal agency is calculated pruning residue according to wavelet tree structure estimates as the new support set Γ=supp (M (c, K)) added, and merges support set Ω=Γ ∪ supp (α _l-1), calculate Signal estimation value ${\left(s\right)}_{\mathrm{\Ω}}={\left({\mathrm{\Θ}}_{\mathrm{i\Ω}}^T{\mathrm{\Θ}}_{\mathrm{i\Ω}}\right)}^{-1}{\mathrm{\Θ}}_{\mathrm{i\Ω}}^{T}y;$

D. according to wavelet tree structure shear signal alpha _l=M (s, K), Optimization of Wavelet tree construction $M(\mathrm{\α},K)=\arg min||\mathrm{\α}-\stackrel{-}{\mathrm{\α}}||,\stackrel{-}{\mathrm{\α}}\∈M_K,$ Upgrade residual error r _l=y-Θ _iα _lif meet stopping criterion for iteration, circulate end, obtains otherwise make l=l+1, return step c, obtained by 16 directions recovering signal is obtained through dual density dual-tree complex wavelet inverse transformation

In described decoding step, by the compression result y got and calculation matrix Φ, by solving obtain compressed sensing image method principle is: be provided with N dimensional signal x ∈ R ^{n × 1}, at certain transform-based Ψ ∈ R ^{n × N}on have the expression-form that K (K<N) is sparse, wherein α (n) represents the coefficient that the n-th base vector be extracted is corresponding.The matrix form of this formula is x=Ψ α, and wherein α is that the vector of N × 1 has K nonzero element.Projected on the calculation matrix Φ of M × N (K<M≤N) by x, obtain the M × 1 vectorial y:y=Φ x=Φ Ψ α be made up of M compressed value, so this signal accurately can be reconstructed out by linear compression.Accurate Reconstruction completes by solving strict combinatorial optimization problem: s.t.y=Φ Ψ α ≡ Θ α.Optimization sparse representation theory shows when matrix Θ meets σ (Θ)>=2K (namely in Θ, 2K row are all linear independences), above l ₀norm optimization problem can uniquely reconstruct, wherein the columns of σ (Θ) the minimal linear relevant group that is matrix Θ.Solving this problem is a np problem, and computation complexity is higher.But research shows, if matrix Φ Ψ meets stronger condition, namely have the equidistant character of constraint (RIP), above-mentioned optimization problem can by l ₀be converted into l ₁the convex optimization problem of constraint obtains unique solution.And if calculation matrix Φ and sparse base Ψ is incoherent, then matrix Θ meets RIP character on very large probability.By what reconstruct obtain recovering signal through inverse wavelet transform, complete reconstruct; Wherein y is the compression result that M × 1 is tieed up, the matrix of y=Φ x, Θ=Φ Ψ to be size be M × N, be coefficient to be estimated, original signal x reconstructs estimated value and is for N × 1 dimensional signal, then will n is reduced to by row ₁× N ₂picture signal, namely complete reduction.

In described step a, utilize dual density dual-tree complex wavelet transform as sparse base Ψ, dual density dual-tree complex wavelet transform to be a kind of redundance be 3 tight frame conversion, its bank of filters is made up of two different dual density wavelet filter groups.As shown in Figure 2, during signal decomposition, two bank of filters process signal three layers of dual density dual-tree complex wavelet transform form simultaneously, do not have exchanges data between two branches.{ h in accompanying drawing 2 _i(n) } be the bank of filters of real part branch, { g _i(n) } be the bank of filters of imaginary part branch, they are all finite impulse response filters.Reconstruction filter banks is made up of the backward of analysis filter bank." dual density " means that each branching filter group is made up of a scaling function and two wavelet functions respectively, and the increase of filtering channel improves design freedom.Dual density two tree small echo combines the advantage of two tree small echo and dual density small echo, is based on two different scaling function φ _h(t), φ _gt small echo ψ that () is different with four _h,i(t), ψ _g,it () (i=1,2) are formed.Wherein ψ _{h, 1}t () is by ψ _{h, 2}(t) skew 0.5.ψ _{g, 1}t () is by ψ _{g, 2}(t) skew 0.5, that is: ψ _{h, 1}(t)=ψ _{h, 2}(t-0.5), ψ _{g, 1}(t)=ψ _{g, 2}(t-0.5).Two small echo ψ _h,i(t), ψ _g,it () (i=1,2) form approximate Hilbert transform pairs (Hilbert Transform Pair), that is: ψ _{g, 1}(t)=H{ ψ _{h, 1}(t) }, ψ _{g, 2}(t)=H{ ψ _{h, 2}(t) }.

Accompanying drawing 3 is directional diagrams of two-dimentional dual density dual-tree complex wavelet transform.Two dimension dual density dual-tree complex wavelet transform eliminates chessboard effect, describe the information of 16 principal directions, and each principal direction has two small echos, respectively as real part and the imaginary part of 16 complex scalar wavelet, more accurate to the feature interpretation of image.

In described step c: prune residue according to wavelet tree structure and estimate as the new support set Γ=supp (M (c, K)) added.The coefficient of picture signal after wavelet transformation can form a tree construction naturally, and maximum wavelet coefficient can along branch's cluster of wavelet tree, one that material is thus formed wavelet coefficient is communicated with tree-model, as shown in Figure 4, wavelet tree structure can perform well in compressed sensing restructing algorithm.Length is N=2 ⁱthe signal x of (I is integer), its wavelet decomposition expression formula can be write as wherein υ is scalar function, ψ _i,jit is wavelet function.If write as x=Ψ α, Ψ is a matrix comprising scalar function and wavelet function, then wavelet coefficient α=[v ₀, ω _0,0, ω _1,0, ω _1,1, ω _2,0...] ^t, define father/minor structure between wherein different wavelet coefficients, namely ω _i,jfather's layer, ω _i+1,2jand ω _i+1,2j+1ω _i,jsublayer.If any one coefficient ω in wavelet tree _i,j∈ Ω (Ω is wavelet coefficient set), so its parent also set omega is belonged to.Utilize wavelet tree structural model can improve image reconstruction quality further.M is compression categorizing selection algorithm, be used for calculating Best tree to be similar to, first calculate in tree with the absolute value of each subtree wavelet coefficient mean value of each node root, using the energy (node that claim this energy maximum be supernode) of the maximal value in absolute value as this node, and retain whole coefficients of subtree corresponding to supernode, optimum subtree set is just made up of these coefficients, thus realizes the thought of tree construction optimum.

In described steps d: according to wavelet tree structure shear signal alpha _l=M (s, K), Optimization of Wavelet tree construction the coefficient of picture signal after wavelet transformation can form a tree construction naturally, and maximum wavelet coefficient can along branch's cluster of wavelet tree, one that material is thus formed wavelet coefficient is communicated with tree-model, as shown in Figure 4, wavelet tree structure can perform well in compressed sensing restructing algorithm.Length is N=2 ⁱthe signal x of (I is integer), its wavelet decomposition expression formula can be write as wherein υ is scalar function, ψ _i,jit is wavelet function.If write as x=Ψ α, Ψ is a matrix comprising scalar function and wavelet function, then wavelet coefficient α=[v ₀, ω _0,0, ω _1,0, ω _1,1, ω _2,0...] ^t, define father/minor structure between wherein different wavelet coefficients, namely ω _i,jfather's layer, ω _i+1,2jand ω _i+1,2j+1ω _i,jsublayer.If any one coefficient ω in wavelet tree _i,j∈ Ω (Ω is wavelet coefficient set), so its parent also set omega is belonged to.Utilize wavelet tree structural model can improve image reconstruction quality further.M is compression categorizing selection algorithm, be used for calculating Best tree to be similar to, first calculate in tree with the absolute value of each subtree wavelet coefficient mean value of each node root, using the energy (node that claim this energy maximum be supernode) of the maximal value in absolute value as this node, and retain whole coefficients of subtree corresponding to supernode, optimum subtree set is just made up of these coefficients, thus realizes the thought of tree construction optimum.

M algorithm comprises the steps:

(1). input B >=0, γ >=0, wherein B is that input data set closes, and γ is iterations, namely chooses at most γ node in tree construction;

(2). initialization v (k) :=B (k), is namely expressed as v (k), n (k) the coefficient value of a kth node :=1, chooses 1 node, suppose that the node chosen at first is not for needing the node chosen, Γ :=0, Γ is loop iteration, suppose that the node chosen at first exists father node, p (k) represents the father node of a kth node;

(3). circulation starts, and finds namely the supernode S finding coefficient value maximum in all supernode S ^*;

(4) if. if i.e. this supernode S ^*father node p (S ^*) be the node that will look for, then arrange Γ :=Γ+n (S ^*), namely obtain according to formula wherein n (S ^*) nodes that comprises for this supernode, otherwise, by S ^*with p (S ^*) merge into 1 new supernode S wherein, v (S)=(v (S ₁) n (S ₁)+v (S ₂) n (S ₂))/(n (S ₁)+n (S ₂)), n (S)=n (S ₁)+n (S ₂), terminate to select, end loop, Output rusults node time, namely the node needed is obtained, supernode S is that node k and its father node p (k) merge the general node formed, and the coefficient value of supernode is defined as v (S)=(B (k)+B [P (k)])/2.

The invention also discloses the structured image compressed sensing restoring system based on dual density dual-tree complex wavelet that a kind of and described structured image compressed sensing method of reducing based on dual density dual-tree complex wavelet is corresponding, comprise as lower module:

Compressed encoding module: for being of a size of N ₁× N ₂two dimensional image be launched into N=N by row ₁× N ₂one-dimensional vector x, the linear compression y=Φ x based on compressed sensing is carried out to one-dimensional vector x, obtains corresponding compression result y, and y and Φ is transferred to decoding unit;

Decoder module: for decode procedure, utilize dual density dual-tree complex wavelet transform as sparse base Ψ, the factor alpha of image under wavelet transformation presents the priori conditions of tree structured feature, decodes in conjunction with CoSaMP algorithm, is below decoding step:

A. extract the high fdrequency component in 16 directions of dual density dual-tree complex wavelet transform, form 16 wavelet basis Ψ _i, i=1 ~ 16, Jacobian matrix Θ _i=Φ Ψ _i;

B. initiation parameter α ₀=0, signal residual error r ₀=y, signal support set l=1, K are signal degree of rarefication;

C. signal agency is calculated pruning residue according to wavelet tree structure estimates as the new support set Γ=supp (M (c, K)) added, and merges support set Ω=Γ ∪ supp (α _l-1), calculate Signal estimation value

D. according to wavelet tree structure shear signal alpha _l=M (s, K), Optimization of Wavelet tree construction $M(\mathrm{\&alpha;},K)=\arg min||\mathrm{\&alpha;}-\stackrel{-}{\mathrm{\&alpha;}}||,\stackrel{-}{\mathrm{\&alpha;}}\&Element;M_K,$ Upgrade residual error r _l=y-Θ _iα _lif meet stopping criterion for iteration, circulate end, obtains otherwise make l=l+1, return step c, obtained by 16 directions recovering signal is obtained through dual density dual-tree complex wavelet inverse transformation.

Main thought of the present invention is: utilize wavelet tree structural sparse model to combine with CoSaMP algorithm, and the coefficient construction model based on dual density dual-tree complex wavelet transform is incorporated above-mentioned algorithm, improve reconstruction property further.

In order to verify feasibility of the present invention and validity, we have carried out emulation experiment by building MATLAB emulation platform, can find out by simulation result the method and system performance advantage compared with prior art that the present invention proposes more intuitively.

Simulated conditions:

(1) image employing size is " Lena " 8bit gray level image of 256 × 256;

(2) calculation matrix chosen is gaussian random matrix, degree of rarefication K=M/4, and iterations is 80 times;

(3) the contrast object condition of emulation experiment is that wavelet basis adopts wavelet transform (DWT) respectively, dual-tree complex wavelet transform (DT-CWT), dual density dual-tree complex wavelet transform (DDDT-CWT), restructing algorithm adopts CoSaMP algorithm and wavelet basis to adopt dual density dual-tree complex wavelet transform (DDDT-CWT), and restructing algorithm adopts based on four kinds of methods such as the structurized CoSaMP of wavelet tree (Tree-CoSaMP) algorithms.

(4) simulation result, accompanying drawing 5 is the relation curve of " Lena " figure reconstructed image average peak signal to noise ratio (PSNR) and average compression factor (MR); Accompanying drawing 6 is " Lena " figure utilizing method of reducing of the present invention and system reconfiguration under MR=0.3 condition.

The invention has the beneficial effects as follows: method and system of the present invention, due to the structural sparse model that utilizes image and have under wavelet transformation and for the defect of wavelet transformation and the dual density dual-tree complex wavelet transform adopted, can obtain higher image reconstruction quality.The method and system that the present invention proposes all have certain advantage compared with classic method from objective evaluation index or subjective vision effect.

Above content is in conjunction with concrete preferred implementation further description made for the present invention, can not assert that specific embodiment of the invention is confined to these explanations.For general technical staff of the technical field of the invention, without departing from the inventive concept of the premise, some simple deduction or replace can also be made, all should be considered as belonging to protection scope of the present invention.

Claims (7)

1., based on a structured image compressed sensing method of reducing for dual density dual-tree complex wavelet, it is characterized in that: described method comprises the steps:

Compressed encoding step: to being of a size of N ₁× N ₂two dimensional image be launched into N=N by row ₁× N ₂one-dimensional vector x, the linear compression y=Φ x based on compressed sensing is carried out to one-dimensional vector x, obtains corresponding compression result y, and y and Φ is transferred to decoder module;

Decoding step: utilize dual density dual-tree complex wavelet transform as sparse base Ψ, the factor alpha of image under wavelet transformation presents the priori conditions of tree structured feature, decodes, specifically comprise the steps: in conjunction with CoSaMP algorithm

A. extract the high fdrequency component in 16 directions of dual density dual-tree complex wavelet transform, form 16 wavelet basis Ψ _i, i=1 ~ 16, Jacobian matrix Θ _i=Φ Ψ _i;

B. initiation parameter α ₀=0, signal residual error r ₀=y, signal support set l=1, K are signal degree of rarefication;

C. signal agency is calculated pruning residue according to wavelet tree structure estimates as the new support set Γ=supp (M (c, K)) added, and merges support set Ω=Γ ∪ supp (α _l-1), calculate Signal estimation value

D. according to wavelet tree structure shear signal alpha _l=M (s, K), Optimization of Wavelet tree construction upgrade residual error r _l=y-Θ _iα _lif meet stopping criterion for iteration, circulate end, obtains otherwise make l=l+1, return step c, obtained by 16 directions recovering signal is obtained through dual density dual-tree complex wavelet inverse transformation

2. compression of images perception method of reducing according to claim 1, is characterized in that: in described decoding step, by the compression result y got and calculation matrix Φ, by solving obtain again by obtain recovering signal through inverse wavelet transform, complete reconstruct; Wherein y is the compression result that M × 1 is tieed up, y=Φ x, Θ _i=Φ Ψ _ithe matrix of to be size be M × N, be coefficient to be estimated, solve this Optimum Solution after, original signal x reconstructs estimated value and is for N × 1 dimensional signal, then will n is reduced to by row ₁× N ₂picture signal.

3. compression of images perception method of reducing according to claim 2, it is characterized in that: in described step a, utilize dual density dual-tree complex wavelet transform as sparse base Ψ, dual density dual-tree complex wavelet transform to be a kind of redundance be 3 tight frame conversion, its bank of filters is made up of two different dual density wavelet filter groups, during signal decomposition, two bank of filters process signal simultaneously, exchanges data is not had between two branches, reconstruction filter banks is made up of the backward of analysis filter bank, " dual density " means that each branching filter group is made up of a scaling function and two wavelet functions respectively, the increase of filtering channel improves design freedom, two dimension dual density dual-tree complex wavelet describes the information of 16 principal directions, and each principal direction has two small echos, respectively as real part and the imaginary part of 16 complex scalar wavelet, more accurate to the feature interpretation of image.

4. compression of images perception method of reducing according to claim 2, it is characterized in that, in described step c: prune residue according to wavelet tree structure and estimate as the new support set Γ=supp (M (c added, K)), the coefficient of picture signal after wavelet transformation can form a tree construction naturally, and maximum wavelet coefficient can along branch's cluster of wavelet tree, one that material is thus formed wavelet coefficient is communicated with tree-model, and it can perform well in compressed sensing restructing algorithm; Wherein, M is compression categorizing selection algorithm, be used for calculating Best tree to be similar to, first calculate in tree with the absolute value of each subtree wavelet coefficient mean value of each node root, using the energy of the maximal value in absolute value as this node, the node claiming this energy maximum is supernode, and retains whole coefficients of subtree corresponding to supernode, optimum subtree set is just made up of these coefficients, thus realizes the thought of tree construction optimum.

5. compression of images perception method of reducing according to claim 2, is characterized in that, in described steps d: according to wavelet tree structure shear signal alpha _l=M (s, K), Optimization of Wavelet tree construction the coefficient of picture signal after wavelet transformation can form a tree construction naturally, and maximum wavelet coefficient can along branch's cluster of wavelet tree, one that material is thus formed wavelet coefficient is communicated with tree-model, and it can perform well in compressed sensing restructing algorithm; Wherein, M is compression categorizing selection algorithm, be used for calculating Best tree to be similar to, first calculate in tree with the absolute value of each subtree wavelet coefficient mean value of each node root, using the energy of the maximal value in absolute value as this node, the node claiming this energy maximum is supernode, and retains whole coefficients of subtree corresponding to supernode, optimum subtree set is just made up of these coefficients, thus realizes the thought of tree construction optimum.

6. the compression of images perception method of reducing according to claim 4 or 5, is characterized in that: M algorithm comprises the steps:

(1). input B >=0, γ >=0, wherein B is that input data set closes, and γ is iterations, namely chooses at most γ node in tree construction;

(2). initialization v (k) :=B (k), is namely expressed as v (k), n (k) the coefficient value of a kth node :=1, chooses 1 node, suppose that the node chosen at first is not for needing the node chosen, Γ :=0, Γ is loop iteration, suppose that the node chosen at first exists father node, p (k) represents the father node of a kth node;

(3). circulation starts, and finds namely the supernode S finding coefficient value maximum in all supernode S ^*;

(4) if. if i.e. this supernode S ^*father node p (S ^*) be the node that will look for, then arrange Γ :=Γ+n (S ^*), namely obtain according to formula wherein n (S ^*) nodes that comprises for this supernode, otherwise, by S ^*with p (S ^*) merge into 1 new supernode wherein, v (S)=(v (S ₁) n (S ₁)+v (S ₂) n (S ₂))/(n (S ₁)+n (S ₂)), n (S)=n (S ₁)+n (S ₂), terminate to select, end loop, Output rusults node time, namely the node needed is obtained, supernode S is that node k and its father node p (k) merge the general node formed, and the coefficient value of supernode is defined as v (S)=(B (k)+B [P (k)])/2.

7. the structured image compressed sensing restoring system based on dual density dual-tree complex wavelet, it is characterized in that: described system comprises compressed encoding module and decoder module, described system performs the structured image compressed sensing method of reducing as described in any one of claim 1-5.