CN107154064A - Natural image compressed sensing method for reconstructing based on depth sparse coding - Google Patents

Abstract

The invention discloses a kind of natural image compressed sensing method for reconstructing based on depth sparse coding, the problem of existing method is difficult to fast, accurately use coefficient reconstruction natural image is mainly solved.Its implementation is：1) to image block and in orthogonal transform domain up conversion, the observation vector of calculation of transform coefficients；2) the recovery conversion coefficient of observation vector is obtained with iteration method, and updates calculating parameter；3) calculate 2) in conversion coefficient observation vector, obtain its with 1) in observation vector residual error amount；4) repeat step 1)-the model that 3) is trained, and preservation model parameter；5) test observation data are input to the model trained with model parameter, image transform coefficients corresponding with test observation data are obtained；6) inverse transformation, the natural image finally rebuild are carried out to the conversion coefficient in 5).The natural image that the present invention is rebuild is clear, and reconstructed velocity is quickly, available for the recovery to natural image.

Description

Natural image compressed sensing method for reconstructing based on depth sparse coding

Technical field

The invention belongs to image processing field, and in particular to a kind of natural image compressed sensing method for reconstructing, available for adopting The natural image of sample recovers.

Background technology

With the development of medium technique, mass image data all suffers from huge challenge in terms of real-time Transmission, storage. The proposition of compressed sensing technology causes these problems to open new thinking in theory, makes problem obtain effective solution.Pressure Contracting perception theory thinks, if signal has openness under a certain kind conversion base, can carry out accidental projection sight to the signal Survey, and Accurate Reconstruction is carried out to it by the prior information of signal with less observation, its model is to solve observation number Norm optimization problem under being constrained according to fidelity.

For above-mentioned compressed sensing model, different norm constraints represents different restructing algorithms and reconstruction property. According to norm, generally using the reconstruct of orthogonal matching pursuit OMP algorithms.Although norm meets compressed sensing model thinking initially Method, that is, find the solution of the optimization problem with minimum degree of rarefication, but because it is a NP-Hard problem, causes the precision of solution It is often not high.Therefore there is scholar to propose to substitute norm so that it becomes convex optimization problem using norm, and propose a series of be based on The restructing algorithm of iteration：Iteration threshold contraction algorithm ISTA, iteratively faster threshold value contraction algorithm FISTA, approximate information transmission are calculated Method AMP etc..Although the proposition of above-mentioned algorithm makes problem further be solved, but they are all based on the solution final accounts of optimum theory Method, however it remains the problems such as reconstruct limited precision, iterative process are complicated, convergence rate is slow.

Recently as the development of depth learning technology, begin with scholar and propose the compressed sensing based on convolutional neural networks Although reconstructing method Recon-Net, this method solves the problem of iterative process is complicated, but still suffers from two problems：1) The reconstructed image noise that direct application model is obtained is larger, it is necessary to can just obtain the preferable reconstructed image of quality by denoising；2) Model convergence rate in training is slower, and on high-performance computer, training pattern is also required to the time of one day.

The content of the invention

It is an object of the invention to for method for reconstructing of the tradition based on optimization and the reconstruction side for being currently based on deep learning The problem of method is present, proposes a kind of natural image compressed sensing method for reconstructing based on depth sparse coding, multiple with simplified model Miscellaneous degree, reduces the training time of model, improves the reconstructed velocity and quality reconstruction of image.

The technical scheme is that：It is pressed by using sparse prior information of the natural image on transform domain Contracting perceptual coding, in conjunction with the approximate information pass-algorithm LAMP based on study and recurrent neural network RNN models, realizing will figure As the restoration and reconstruction of coding information, implementation step includes as follows：

(1) model training step：

(1a) inputs plurality of pictures, and takes from these pictures n training image blocks X；

(1b) is compressed perception observation to n training image blocks X in (1a), obtains n observed differential Y, and use this A little training image blocks constitute n training sample pair with corresponding observed differential：{ (X=x₁,x₂,...,x_n-1,x_n), (Y=y₁, y₂,...,y_n-1,y_n)}；

(1c) sets model training number of times K=100, randomly selects r training sample y from Y, X every time_r、x_r, and use Gradient descent method is trained, and the cut-off condition flag trained every time is that 50 model error values of iteration are unattenuated；

(1d) sets the parameter of sparse coding algorithm, initializes iterations T=10, and make initial transformation systemSee Survey data residual error v^t=y, whereinFor the training image block conversion coefficient of the t times iterative calculation, v^tFor the observation of the t times iteration Residual error；

(1e) calculates the training image block conversion coefficient of the t+1 times iteration：WhereinFor The conversion coefficient of the t times iteration, A^TC^tv^tFor the conversion coefficient of the observation residual error of the t times iteration, A^TIt is observing matrix A transposition, C^tIt is the t times parameter matrix to be optimized,For the threshold value of the t times iteration, α^tIt is the scalar ginseng of the t times renewal Numerical value, M is the dimension for observing data y, | | v^t||₂Represent v^tTwo norms, η_st() is threshold value contracting function；

(1f) calculates the observation residual error of the t+1 times iteration：Wherein, b^t+1v^tIt is Onsagercorrection；

(1g) circulation performs T (1e)-(1f) and obtains conversion coefficient

The conversion coefficient that (1h) is obtained as (1g)When meeting iteration cut-off condition flag, the model ginseng of this training is preserved Number；

(1i) circulation performs K (1d)-(1h), completes model training；

(2) testing procedure：

(2a) will observe data y_testAnd the T parameter matrix obtained by model trainingWith scalar parameter valueIt is input in the model trained, obtains and input observation data y_testCorresponding test image conversion coefficient

(2b) is to conversion coefficientPCA inverse transformations are done, are obtained and observation data y_testCorresponding image Img：Wherein, Ψ^-1Represent PCA inverse-transform matrixs；

(2c) converts the Ψ Ψ for possessing orthogonality and existing according to PCA^-1=Ψ Ψ^TRelation, will be with observation data y_testIt is right The image Img answered is rewritten as：Complete paired observations y_testNatural image rebuild, wherein, Ψ^TRepresent PCA Direct transform matrix Ψ transposition.

The present invention has advantages below compared with other prior arts：

Firstth, present invention introduces the sparse prior information of natural image, with reference to the excellent of deep neural network and sparse coding Gesture, reduces model complexity, so as to reduce the reconstruction time of image, realizes the quick reconstruction of compressed sensing, and carry The high reconstruction effect of natural image；

Secondth, the present invention improves model training speed, so that implementation model using the model training method of transfer learning Fast Training.

Brief description of the drawings

Fig. 1 realizes general flow chart for the present invention's；

Fig. 2 is the model training sub-process figure in the present invention；

Fig. 3 is the image reconstruction sub-process figure in the present invention；

Fig. 4 is Barbara primitive natures image used in emulation experiment of the present invention；

Fig. 5 is the reconstruction design sketch to Barbara images when compression ratio is 0.25 with existing TVAL3 methods；

Fig. 6 is the reconstruction design sketch to Barbara images when compression ratio is 0.25 with existing Recon-Net methods；

Fig. 7 is the reconstruction design sketch to Barbara images when compression ratio is 0.25 with the present invention.

Embodiment：

Embodiments of the invention and effect are described in detail below in conjunction with accompanying drawing：

Reference picture 1, the natural image method for reconstructing of the invention based on depth sparse coding, including model training and test two Part.N training image blocks X is inputted first and training sample pair is constructed, and then carries out the model that model training is trained, Test observation data input is tested into the model trained again, the natural image rebuild.

The model training of the present invention is described in detail with this two parts is tested below：

First, model training part

Reference picture 2, this part realizes that step is as follows：

Step 1：N training image blocks X is inputted, training sample pair is obtained,

(1a) inputs n training image blocks X, to the training image blocks data x of each input_iCarry out principal component analysis PCA Conversion, obtains conversion coefficientWherein, Ψ represents principal component analysis PCA direct transform matrixes, according to principal component point The orthogonality of PCA conversion is analysed, Ψ Ψ are obtained^-1=Ψ Ψ^TRelational expression, drawn according to relational expressionWherein, Ψ^-1And Ψ^TPrincipal component analysis PCA inverse-transform matrixs and direct transform matrix Ψ transposition are represented respectively；

(1b) is observed according to compressed sensing observation model to each training image blocks, obtains observation data y_i：Wherein, A=Φ Ψ^T, Φ is lack sampling gaussian random observing matrix, and vectorial w is the white Gaussian with zero-mean Noise；

N training image blocks X is constituted n training sample pair by (1c) with corresponding n observed differential Y：{ (X=x₁, x₂,...,x_n-1,x_n), (Y=y₁,y₂,...,y_n-1,y_n)}。

Step 2：Model training number of times is set, r training sample pair is randomly selected,

(2a) sets model training number of times K=100；

(2b) randomly selects r training sample to { x when training every time from Y, X_r,y_r}。

Step 3：Correlated variables in the parameter of sparse coding algorithm, initialization algorithm is set.

(3a) initialization iterations T=10；

(3b) makes initial transform coefficientObserve data residual error v^t=y, whereinFor the image of the t times iterative calculation Block conversion coefficient, v^tFor the observation residual error of the t times iteration.

Step 4：Calculate the training image block conversion coefficient of the t+1 times iteration

(4a) calculates the observation residual error v of the t times iteration^tSparse coefficient A^TC^tv^t, wherein A^TIt is observing matrix A transposition, C^tIt is the t times parameter matrix to be optimized and is initialized as unit matrix；

(4b) calculates the training image blocks sparse coefficient of the t+1 times iteration,Wherein,For the t times The conversion coefficient of iteration,For the threshold value of the t times iteration, α^tIt is the scalar parameter value of the t times renewal, M is observation Data y dimension, | | v^t||₂Represent v^tTwo norms；

(4c) calculates the training image block conversion coefficient of the t+1 times iteration,

Wherein, η_st() is threshold value contracting function, for by threshold value λ^tWith sparse coefficient μ^t+1It is compared, specific method It is that will be less than threshold value λ^tSparse coefficient μ^t+1Zero setting, will be greater than threshold value λ^tSparse coefficient μ^t+1It is set to μ^t+1With threshold value λ^tDifference Absolute value.

Step 5：Calculate the observation residual error v of the t+1 times iteration^t+1。

(5a) first obtains step 4In be more than zero coefficient and be set to 1, then it is averaged by row, obtained Zero normWeight b is calculated again^t+1：

Wherein N is conversion coefficientDimension, M is observation residual error v^tDimension；

(5b) is by weight b^t+1With observation residual error v^tDot product is carried out, Onsager correction matrix b is obtained^t+1v^t；

The matrix b that (5c) will be obtained in (5b)^t+1v^tSubstitute into formulaCalculate the t+1 times iteration Observe residual error v^t+1, wherein y is that training image blocks observe data, and A is observing matrix.

Step 6：Step 4-step 5 circulation is performed T=10 times, conversion coefficient is obtained

Step 7：Preserve the model parameter of this training.

The conversion coefficient obtained when step 6When meeting iteration cut-off condition flag, the model parameter of this training is preserved, Wherein, the cut-off condition flag trained every time is that 50 model error values of iteration are unattenuated.

Step 8：Circulation performs K step 3-step 7, completes model training.

2nd, part of detecting

Reference picture 3, this part realizes that step is as follows：

Step 9：The parameter that data and model training part are preserved is observed in input test, obtains input observation data y_testIt is right The image transform coefficients answered

T Matrix C of its preservation is taken out from model training part^tAnd scalar ce^tIt is designated as respectivelyWithAnd will The test observation data y collected in the two parameters and reality scene_testAs input, it is input in the model trained, Output and observation data y_testCorresponding image transform coefficients

Step 10：Observation data y is obtained by principal component analysis PCA inverse transformations_testCorresponding natural image Img.

(10a) is to conversion coefficientPrincipal component analyzes PCA inverse transformations, obtains and observation data y_testCorresponding nature Image：Wherein, Ψ^-1Represent principal component analysis PCA inverse-transform matrixs；

The Ψ Ψ that (10b) is converted according to principal component analysis PCA^-1=Ψ Ψ^TRelational expression, will be with observation data y_testIt is corresponding Natural image Img is rewritten as：Complete paired observations y_testNatural image rebuild, wherein, Ψ^TRepresent master Constituent analysis PCA direct transform matrixes Ψ transposition.

The effect of the present invention can be illustrated by following emulation experiment：

1st, simulated conditions：

1) programming platform used in emulation experiment is Pycharm v2016；

2) the natural image data used in emulation experiment come from standard exercise, test data set；

3) the training image block size used in emulation experiment is 25 × 25, and number of training n is 52650；

4) in emulation experiment, compressed sensing experimental result, Y-PSNR are evaluated using Y-PSNR PSNR indexs PSNR is defined as：

Wherein, MAX_iAnd MSE_iTo rebuild high-resolution natural image Img out max pixel value and mean square error, N For number of pixels.

2nd, emulation content：

Emulation 1, using TVAL3 methods, rebuilds, it is rebuild to natural image Barbara when compression ratio is 0.25 As a result it is as shown in Figure 5.

Emulation 2, using Recon-Net methods, rebuilds to natural image Barbara when compression ratio is 0.25, its Reconstructed results are as shown in Figure 6.

Emulation 3, using the inventive method, rebuilds, it is rebuild to natural image Barbara when compression ratio is 0.25 As a result it is as shown in Figure 7.

The present invention, which is can be seen that, from the natural image Barbara reconstructed results shown in Fig. 5-Fig. 7 reconstructs next image More apparent than the image that other method is reconstructed, image border is sharper keen, and visual effect is more preferable.

By existing TVAL3 methods, NLR-CS methods, Recon-Net methods and the inventive method respectively to natural image Barbara carries out Reconstruction Simulation, obtained Y-PSNR PSNR, as shown in table 1..

The PSNR values of the different method for reconstructing of table 1

As it can be seen from table 1 the Y-PSNR PSNR of the present invention is 0.25 in compression ratio than existing TVAL3 methods When high 3.73dB, to be higher by 2.00dB than existing Recon-Net.

Claims (3)

1. the natural image method for reconstructing based on depth sparse coding, including：

(1) model training step：

(1a) inputs plurality of pictures, and takes from these pictures n training image blocks X；

(1b) is compressed perception observation to n training image blocks X in (1a), obtains n observed differential Y, and instructed with these Practice image block and constitute n training sample pair with corresponding observed differential：{ (X=x₁,x₂,...,x_n-1,x_n), (Y=y₁,y₂,..., y_n-1,y_n)}；

(1c) sets model training number of times K=100, randomly selects r training sample y from Y, X every time_r、x_r, and use gradient Descent method is trained, and the cut-off condition flag trained every time is that 50 model error values of iteration are unattenuated；

(1d) sets the parameter of sparse coding algorithm, initializes iterations T=10, and make initial transformation systemObserve number According to residual error v^t=y, whereinFor the training image block conversion coefficient of the t times iterative calculation, v^tFor the observation residual error of the t times iteration；

(1e) calculates the training image block conversion coefficient of the t+1 times iteration：WhereinFor t The conversion coefficient of secondary iteration, A^TC^tv^tFor the conversion coefficient of the observation residual error of the t times iteration, A^TIt is observing matrix A transposition, C^tIt is The t times parameter matrix to be optimized,For the threshold value of the t times iteration, α^tIt is the scalar parameter value of the t times renewal, M is the dimension for observing data y, | | v^t||₂Represent v^tTwo norms, η_st() is threshold value contracting function；

(1f) calculates the observation residual error of the t+1 times iteration：Wherein, b^t+1v^tIt is Onsager Correction；

(1g) circulation performs T (1e)-(1f) and obtains conversion coefficient

The conversion coefficient that (1h) is obtained as (1g)When meeting iteration cut-off condition flag, the model parameter of this training is preserved；

(1i) circulation performs K (1d)-(1h), completes model training；

(2) testing procedure：

(2a) will observe data y_testAnd the T parameter matrix obtained by model trainingWith scalar parameter value It is input in the model trained, obtains and input observation data y_testCorresponding test image conversion coefficient

(2b) is to conversion coefficientPCA inverse transformations are done, are obtained and observation data y_testCorresponding image Img： Wherein, Ψ^-1Represent PCA inverse-transform matrixs；

(2c) converts the Ψ Ψ for possessing orthogonality and existing according to PCA^-1=Ψ Ψ^TRelation, will be with observation data y_testCorresponding figure As Img is rewritten as：Complete paired observations y_testNatural image rebuild, wherein, Ψ^TRepresent PCA direct transforms Matrix Ψ transposition.

2. perception in accordance with the method for claim 1, is compressed to n image block X in (1a) wherein in step (1b) Observation, is carried out as follows：

(1b1) is to each image block data x_iPCA conversion is carried out, conversion coefficient is obtained：Wherein, Ψ and Ψ^-1Difference table Show PCA direct transforms and its inverse transformation, simultaneously because the orthogonality of PCA conversion, meets Ψ Ψ^-1=Ψ Ψ^T, then have,Ψ^TRepresent PCA direct transform matrixes Ψ transposition；

(1b2) is observed according to compressed sensing observation model to each image block, obtains observing data：Wherein A=Φ Ψ^T, matrix Φ is lack sampling gaussian random observing matrix, and vectorial w is the white Gaussian noise with zero-mean.

3. according to the method described in claim (1), correction b of Onsager wherein in step (1f)^t+1v^t, press Following steps are calculated：

(1f1) first willIn be more than zero coefficient and be set to 1, then it is averaged by row, obtainedZero normMost Weight b is calculated afterwards^t+1：

<mrow> <msup> <mi>b</mi> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mfrac> <mi>N</mi> <mi>M</mi> </mfrac> <mo>|</mo> <mo>|</mo> <msup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>|</mo> <msub> <mo>|</mo> <mn>0</mn> </msub> <mo>,</mo> </mrow>

Wherein, N is conversion coefficientDimension, M is observation residual error v^tDimension；

(1f2) is by weight b^t+1With observation residual error v^tDot product is carried out, Onsager correction matrix b is obtained^t+1v^t。