CN103985100A - Partitioned compression sensing method based on self-adaptive observation combinational optimization - Google Patents

Abstract

The invention provides a partitioned compression sensing method based on self-adaptive observation combinational optimization and belongs to the field of the signal processing technology. The partitioned compression sensing method is used for solving the problem that the quality of image reconstruction in a partitioned compression sensing algorithm is reduced badly compared with compression sensing. The method includes the steps that on the basis of image portioning, according to difference of sparsity of image blocks, the image blocks are observed in a self-adaptive mode through different observation matrixes; through effect comparison of reconstructed image blocks, an observation with optimal reconstruction is selected as the optimal observation of the current image block, and optimal observations of all the image blocks are combined to obtain a combinational optimization observation; finally, an original image is reconstructed through the obtained combinational optimization observation. The real-time performance of the algorithm is superior to that of compression sensing; meanwhile, the defect that the quality of a partitioned compression sensing image is reduced in the image reconstruction process is overcome. Through the method, in the application field, signals can be rapidly propagated, and the reliable signal quality is provided. In addition, information after combinational optimization observations can be used as features, and the method has high reference value in the machine learning field.

Description

A kind of piecemeal compression sensing method based on adaptive observation Combinatorial Optimization

Technical field

The present invention relates to signal processing technology field, the particularly compressed sensing of signal, specifically refers to a kind of piecemeal compression sensing method based on adaptive observation Combinatorial Optimization.

Background technology

In the common method of image Compression, first image will, with a higher sampling rate, meet nyquist sampling theorem and sample, and converts digital format to, then carries out compressed encoding by standards such as JPEG.But this method is also inapplicable on the equipment such as sensor low-power, low resolution.In recent years, the breakthrough research of Candes and Donoho, compressed sensing (Compressed Sensing has been proposed, be abbreviated as CS) theoretical method, overcome the restriction of nyquist sampling theorem, meet at signal on the basis of sparse property, can go out original signal by Accurate Reconstruction with a small amount of observation, thus the problem of effectively having avoided traditional images compressed encoding to exist.

In recent years, no matter compressed sensing is aspect theoretical research, or aspect practical application, has all obtained huge progress.Some well-known enterprise institutions such as the well-known universities and colleges of many countries such as the U.S., European Countries and China and Intel, Google, Bell Laboratory have successively added the research to compressive sensing theory.In practical application, in biomedicine, compressed sensing can be applicable to Magnetic resonance imaging aspect.Aspect radar imagery, can effectively reduce the data transfer rate of high-resolution radar imaging system by the irrelevant observation process of utilization compressed sensing, be expected to solve collection, storage and the transmission problem of super large data volume in radar system.In recognition of face, the feature extraction by applied compression perception to facial image, has improved the precision of identification.It is found that and utilize compression sensing method, in sampling process, need to once carry out sampling processing to entire image, this has reduced the real-time of system.Meanwhile, when entire image is used to compressed sensing reconstruct, operand is also quite large.Therefore, Lu Gan has proposed piecemeal compressed sensing (Block Compressed Sensing, BCS) method.The method is that image is divided into many, when observation and reconstruct, separately each image block is operated, and strengthens the real-time to image processing, its computation complexity reduces greatly, and because piecemeal observing matrix dimension reduces greatly, be beneficial to storage, but Image Reconstruction precision needs to improve.

Summary of the invention

The present invention be directed to the problem that BCS differs from than CS aspect Image Reconstruction precision, on BCS algorithm basis, make improvements piecemeal compressed sensing (Self-Adaptive Measurement Combinatorial Optimization-BCS, the is abbreviated as AMCO-BCS) algorithm that obtains adaptive observation Combinatorial Optimization.AMCO-BCS method is the scheme of a kind of neutralization of CS and BCS.On the good basis of real-time, ensure the reconstruction quality of image.

AMCO-BCS algorithm is on the basis of image block, according to the sparse property difference of different masses, is meeting under restricted constraint condition, selects adaptively different observation dimensions.Then, utilize different observing matrixes to observe same image block, obtain respectively the observed reading of this image block, the observed reading that recycles the different observing matrixes of this image block is reconstructed, and the observed reading that choice accuracy is larger is observed as the optimum of this piece.By this Combinatorial Optimization mode, obtain good observed reading.Finally, utilize the observed reading obtaining to be reconstructed image.Its overall flow figure as shown in Figure 1.

Technical scheme provided by the invention is as follows:

A piecemeal compression sensing method based on adaptive observation Combinatorial Optimization, comprises following step:

Step 1: image sparse judgement.Suppose that X represents original image, image X is carried out to wavelet transformation: X=ψ θ, wherein ψ is the sparse transformation matrix of small echo.If θ is sparse, continue (2) step; Otherwise image X is not processed.

Step 2: image block.Original image X described in step 1 is divided into B × B piece, uses x _i(i=1,2 ..., B × B) i piece after presentation video piecemeal;

Step 3: the observing matrix that produces adaptively each image block.First each image block is produced to two different random observation matrixes, use φ ₁ ⁱand φ ₂ ⁱ(i=1,2 ..., B × B) represent respectively correspondence image piece x _i(i=1,2 ..., B × B) two different random observation matrixes.Based on Correlation Theory, the irrelevant condition of sparse transformation matrix and observing matrix can be equivalent to Gramma matrix (A ^cS) ^ta ^cSunit matrix approximation problem:

Wherein Φ is random observation matrix, and ψ is the sparse transformation matrix of small echo, and I is unit matrix, (A ^cS) ^trepresent A ^cStransposition, substitution image block x _irandom observation matrix φ ₁ ⁱand φ ₂ ⁱand the sparse transformation matrix ψ of the small echo of this image block _i, utilizing the sparse transformation matrix of small echo of signal is an optimization observing matrix lower than sparse transformation matrix correlativity by random observation matrix by training study.KSVD method by M Aharon solves above formula, can obtain definite observing matrix.Utilize the method, same image block is produced to two different adaptive observation matrix φ _1i, φ _2i(i=1,2 ..., B × B).

Step 4: each image block is optimized to observation, obtains the optimum observation of each image block and the Combinatorial Optimization observed result of entire image.Specifically be divided into the following steps:

● two observing matrix φ that obtain by step 3 _1i, φ _2irespectively to image block x _iobserve, obtain image block x _iobserved reading:

y _ji＝φ _jix _i

Wherein i=1,2 ..., B × B, j=1,2.

● according to image block x _itwo observed reading y _1iand y _2i, the linear prediction method based on minimizing mean square deviation that uses Lu GanF to propose is reconstructed each image block respectively.Reconstructing method is as follows:

$\min {\left|\right|x_i-{\hat{x}}_{\mathrm{ji}}\left|\right|}_2^2$

Wherein, ${\hat{x}}_{\mathrm{ji}}={\widehat{\mathrm{\φ}}}_B{y}_{\mathrm{ji}}$

Wherein i=1,2 ..., B × B, j=1,2, r _xxrepresent the autocorrelation function of original signal, φ _brepresent observing matrix.

● select the optimum observed reading of the less corresponding observation of reconstruction result of Y-PSNR as this image block, the optimum observation of each image block is combined, obtain the Combinatorial Optimization observation y=[y of entire image ₁, y ₂... y _i..., y _{b × B}].

Step 5: utilize the Combinatorial Optimization observation obtaining to be reconstructed original image.Adopt reconstructing method with the reconstructing method in step 4, Lu GanF propose the linear prediction method based on minimizing mean square deviation:

$\min {\left|\right|x_i-{\hat{x}}_i\left|\right|}_2^2$

Wherein, ${\hat{x}}_i={\widehat{\mathrm{\φ}}}_B{y}_i,(i=\mathrm{1,2},...,B\×B)$

Wherein r _xxrepresent the autocorrelation function of original signal, φ _brepresent observing matrix.In natural image, R _xxadopt AR (1) model, wherein coefficient of autocorrelation ρ=0.95.

Brief description of the drawings

Fig. 1 algorithm overall flow figure

The former figure of Fig. 2 lena test pattern

Lena figure after Fig. 3 wavelet transformation

Fig. 4 AMCO-BCS reconstruct lena figure

Fig. 5 BCS1 reconstruct lena figure

Fig. 6 BCS2 reconstruct lena figure

Fig. 7 CS, BCS, the sampling rate under AMCO-BCS and PSNR graph of a relation.

Embodiment

Below in conjunction with accompanying drawing, embodiments of the invention are elaborated.The present embodiment is implemented under taking technical solution of the present invention as prerequisite, provided detailed embodiment and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

Suppose that X represents original image, X is divided into B × B, use x _i(i=1,2 ..., B × B) i piece after presentation video piecemeal.The wavelet transform matrix of ψ presentation video X; ψ _i(i=1,2 ..., B × B) represent the wavelet transform matrix of i image block; φ ₁ ⁱ, φ ₂ ⁱ(i=1,2 ..., B × B) expression correspondence image piece x _i(i=1,2 ..., B × B) two different random observation matrixes; φ _1i, φ _2i(i=1,2 ..., B × B) represent by φ ₁ ⁱ, φ ₂ ⁱthe correspondence image piece x producing _iadaptive observation matrix; y _1i, y _2irepresent to utilize respectively φ _1i, φ _2ito same image block x _ithe observed quantity obtaining after observing.Y _iequal y _1i, y _2imiddle reconstructed error is less.Y represents to utilize the final observed quantity obtaining after adaptive observation Combinatorial Optimization.PSNR _1i, PSNR _2irepresent to utilize respectively φ _1i, φ _2ito same image block x _ithe Y-PSNR being reconstructed.Implementation process is as follows:

Start

1. couple image X carries out wavelet transformation: X=ψ θ

If θ is sparse, continue; Otherwise jump out.The present embodiment is tested taking lena figure (Fig. 2) as sample, and it is carried out to image after wavelet transformation as shown in Figure 3, and most elements value is 0, is therefore sparse.

2. by image array piecemeal: X → x _i(i=1,2..., B × B).

3.for?i＝ltoB×B{

(1) produce wavelet transform matrix: ψ _i(i=1,2 ..., B × B);

(2) produce in accordance with the following steps adaptive observation matrix φ _1i, φ _2i(i=1,2 ..., B × B):

A) initialization random observation matrix φ ₁ ⁱ

B) by Φ=φ ₁ ⁱ, ψ=ψ _isubstitution following formula:

Solve and obtain determinacy observing matrix φ _1i;

φ _2ithe same φ of the mode that obtains _1i;

(3) observation: y _1i=φ _1ix _i, y _2i=φ _2ix _i

(4) reconstruct: x _i← y _1i, x _i← y _2i

(5) calculate PSNR _1ipSNR _2i

}

4.if?PSNR _1i＜PSNR _2i，y _i＝y _2i；else，y _i＝y _1i；

5. obtain Combinatorial Optimization observation y=[y ₁, y ₂... y _i..., y _{b × B}];

6. adopt the linear prediction method reconstructed image based on minimizing mean square deviation:

$\min {\left|\right|x_i-{\hat{x}}_i\left|\right|}_2^2$

Wherein, ${\hat{x}}_i={\widehat{\mathrm{\φ}}}_B{y}_i,(i=\mathrm{1,2},...,B\×B)$

Wherein r _xxrepresent the autocorrelation function of original signal.In natural image, R _xxadopt AR (1) model, wherein coefficient of autocorrelation ρ=0.95.

}

Utilize the reconstruct lena that AMCO-BCS algorithm obtains to scheme as shown in Figure 4; Adopt two different observing matrixes, the restructuring graph respectively lena figure application BCS being obtained as shown in Figure 5 and Figure 6.Under different sampling rates, conventional compression perception, piecemeal compressed sensing, contrast as shown in Figure 7 with the PSNR of AMCO-BCS of the present invention

As seen from the figure, the reconstruction accuracy of the AMCO-BCS that the present invention proposes is better than BCS, and poorer than CS.Simulation result in other natural images is also like this.And aspect real-time, because first AMCO-BCS carries out piecemeal to image, then every is processed, therefore in the time that not transmitting completely, just can process it image, so real-time aspect is better than CS, and because its algorithm is than BCS complexity, therefore its real-time is slightly poorer than BCS.Can say, AMCO-BCS method in this paper is the scheme of a kind of neutralization of CS and BCS.On the good basis of real-time, ensure the reconstruction quality of image.

Claims (2)

1. the piecemeal compression sensing method based on adaptive observation Combinatorial Optimization, is characterized in that, described method comprises the following steps:

(1) image sparse judgement: suppose that X represents original image, image X is carried out to wavelet transformation, X=ψ θ, wherein ψ is the sparse transformation matrix of small echo, if θ is sparse, continues (2) step, otherwise image X is not processed;

(2) image block: the original image X described in (1) is divided into B × B piece, uses x _i(i=1,2 ..., B × B) i piece after presentation video piecemeal;

(3) produce adaptively the observing matrix of each image block: first each image block is produced to two different random observation matrixes, use φ ₁ ⁱand φ ₂ ⁱ(i=1,2 ..., B × B) represent respectively correspondence image piece x _i(i=1,2 ..., B × B) two different random observation matrixes, based on Correlation Theory, the irrelevant condition of sparse transformation matrix and observing matrix can be equivalent to Gramma matrix (A ^cS) ^ta ^cSunit matrix approximation problem:

Wherein Φ is random observation matrix, and ψ is the sparse transformation matrix of small echo, and I is unit matrix, (A ^cS) ^trepresent A ^cStransposition, substitution image block x _irandom observation matrix φ ₁ ⁱand φ _a ⁱand the wavelet transform matrix ψ of this image block _iutilize the sparse transformation matrix of small echo of signal, be an optimization observing matrix lower than sparse transformation matrix correlativity by random observation matrix by training study, KSVD method by M Aharon solves above formula, can obtain definite observing matrix, utilize the method, same image block is produced to two different adaptive observation matrix φ _1i, φ _2i(i=1,2 ..., B × B);

(4) Combinatorial Optimization observation: each image block is optimized to observation, obtains the optimum observation of each image block and the Combinatorial Optimization observed result of entire image;

(5) utilize the Combinatorial Optimization observation obtaining to be reconstructed original image: the reconstructing method of employing is the linear prediction method based on minimizing mean square deviation that Lu GanF proposes, that is:

$\min {\left|\right|x_i-{\hat{x}}_i\left|\right|}_2^2$

Wherein, ${\hat{x}}_i={\widehat{\mathrm{\φ}}}_B{y}_i,(i=\mathrm{1,2},...,B\×B)$

Wherein r _xxrepresent the autocorrelation function of original signal, φ _brepresent observing matrix.

2. the piecemeal compressed sensing based on adaptive observation Combinatorial Optimization according to claim 1, is characterized in that, described Combinatorial Optimization observation procedure is as follows:

(1) right to use requires two observing matrix φ that in 1, step (3) obtains _1i, φ _2irespectively to image block x _iobserve, obtain image block x _iobserved reading:

y _ji＝φ _jix _i

Wherein i=1,2 ..., B × B, j=1,2;

(2) according to image block x _itwo observed reading Y _1iand y _2i, use the linear prediction method based on minimizing mean square deviation, respectively each image block is reconstructed, reconstructing method is as follows:

$\min {\left|\right|x_i-{\hat{x}}_{\mathrm{ji}}\left|\right|}_2^2$

Wherein, ${\hat{x}}_{\mathrm{ji}}={\widehat{\mathrm{\φ}}}_B{y}_{\mathrm{ji}}$

Wherein i=1,2 ..., B × B, j=1,2, r _xxrepresent the autocorrelation function of original signal, φ _brepresent observing matrix;

(3) the corresponding observation of reconstruction result that selection Y-PSNR is less, as the optimum observed reading of this image block, is combined the optimum observation of each image block, obtains the Combinatorial Optimization observation y=[y of entire image ₁, y ₂... yi..., y _{b × B}].