CN103237205B - Digital camera based on Toeplitz matrix observation and dictionary learning compresses formation method - Google Patents

Abstract

The invention discloses a kind of digital camera based on Toeplitz matrix observation and dictionary learning compression formation method, mainly to solve in existing method because the problem of gaussian random observing matrix more difficult realization in actual applications.Its implementation procedure is: first design the code-disc before digital camera lens, then try to achieve the point spread function in real application systems, obtain corresponding Toeplitz observing matrix, carry out observation obtain a small amount of measured value to real image.Finally all kinds of geometry image block sample is used to the method training redundant dictionary of KSVD dictionary learning, and reconstruct by block in conjunction with nonlinear reconstruction algorithm, the image block reconstructed the most at last is combined into reconstructed image.The present invention, under low sampling rate, improves the quality of reconstruct, under different sample rate, all can reach good quality reconstruction to various natural image, can be used in actual digital camera compression imaging system.

Description

Digital camera based on Toeplitz matrix observation and dictionary learning compresses formation method

Technical field

The invention belongs to technical field of image processing, relate to a kind of compression formation method based on Toeplitz matrix observation and dictionary learning, can be used in digital camera imaging and Airborne Camera imaging process.

Background technology

Traditional signal sampling theory take nyquist sampling theorem as standard, and for ensureing undistorted ground restoring signal from sampled signal, sample frequency at least should be greater than the twice of signal cut-off frequency.When signal bandwidth is larger, traditional sampling theory causes higher hardware costs, brings immense pressure to storage and transmission simultaneously.Compressed sensing technology CS is exactly the theoretical frame in order to overcome a kind of new signal acquisition that this problem proposes and process.Its basic thought is: suppose that original signal is compressible, namely rarefaction representation can be obtained under certain dictionary, then by structure one and the incoherent observation system of dictionary, with observing matrix, signal is carried out to primary signal, under little observation, just can recover primary signal.Under this theoretical frame, the bandwidth of sample rate and signal has nothing to do, relevant with content with the structure of information in signal.

One of technology of key in compressed sensing technology is exactly observation, under the precondition of openness priori more afterwards, can be reconstructed by optimized algorithm to signal.What relatively effectively also relatively commonly use in compressive sensing theory is gaussian random observing matrix, and the gaussian random observing matrix of Normal Distribution proves can meet RIP criterion preferably in theory, can reconstruct primary signal with high probability.But gaussian random observing matrix has some limitations in actual applications, constrain the practical application of compressed sensing technology to a great extent.

Summary of the invention

The object of the invention is to the shortcoming overcoming above-mentioned prior art, propose a kind of digital camera based on Toeplitz matrix observation and dictionary learning and compress formation method, to solve the problem that gaussian random observing matrix is difficult to be applied to real system.

Realizing the object of the invention technical thought is: by designing the code-disc of digital camera, generate Toeplitz observing matrix, adopt and sample lower than Nyquist sampling rate, method in conjunction with dictionary learning improves the reconstruct probability of original image signal, and especially under low sampling rate, comparatively gaussian random observing matrix has better quality reconstruction.Its concrete steps comprise as follows:

(1) design the code-disc of digital camera, the place that code-disc is closed is 0, and the place of opening is 1;

(2) according to the code-disc of design, try to achieve the point spread function p in this camera real system, obtain the frequency domain response of camera wherein for Fourier transform matrix, the element in matrix M is pulled into diagonal matrix C _m;

(3) by diagonal matrix C _mobtain new Toeplitz matrix: carry out down-sampling operation to Toeplitz matrix B, obtain the observing matrix in actual camera system: R=DB, wherein D is down-sampling matrix, for inverse Fourier transform;

(4) by observing matrix R and original image signal f, measured value is obtained: y=Rf;

(5) original image signal f is divided into the image fritter of the 16*16 of non-overlapping copies, each image fritter is denoted as f respectively _i', i=1,2...n, wherein n is the number of image fritter;

(6) measured value of each image fritter is calculated: y _i'=Rf _i', i=1,2...n;

(7) follow the trail of BP restructing algorithm by base, solve the sparse coefficient of corresponding image fritter i=1,2...n;

(8) according to sparse coefficient reconstruct each image fritter: i=1,2...n, wherein D is sparse dictionary;

(9) by all reconstruct small images x _icombination obtains reconstructed image X '.

The present invention has the following advantages compared with prior art:

1. compressed sensing technology is applied in digital camera compression imaging process by the present invention, adopts and samples lower than Nyquist sampling rate, can represent original image signal with less sampling number, is convenient to store and transmission.

2. the present invention is by adding code-disc before logarithmic code camera lens, Toeplitz observing matrix is applied in digital camera compression imaging process, solve the problem of more difficult realization in the practical application of random Gaussian observing matrix, comparatively random Gaussian observing matrix has better quality reconstruction, and can obtain reconstructing more accurately in conjunction with the method for dictionary learning.

3. the present invention adds code-disc before digital camera lens, makes light generation aliasing, and the information that just can obtain original image signal by the transducer CCD of lesser amt, adds the useful life of CCD.

4. picture signal is carried out linear superposition by the Toeplitz observing matrix in the present invention, if the compressed signal after superposition is intercepted and captured by other people in transmitting procedure, when the other side does not know observing matrix concrete form, cannot original image signal be parsed, therefore increase the fail safe in image signal transmission process.

Accompanying drawing explanation

Fig. 1 is general flow chart of the present invention;

Fig. 2 is the natural image of Lena, Camera, Peppers and House;

Fig. 3 is the reconstruction result figure sampled to the nyquist sampling rate that Lena image carries out 40% with gaussian random observing matrix and the present invention;

Fig. 4 is the reconstruction result figure sampled to the nyquist sampling rate that Camera image carries out 40% with gaussian random observing matrix and the present invention;

Fig. 5 is the reconstruction result figure sampled to the nyquist sampling rate that Peppers image carries out 40% with gaussian random observation and the present invention;

Fig. 6 is the reconstruction result figure sampled to the nyquist sampling rate that House image carries out 40% with gaussian random observation and the present invention;

Fig. 7, when carrying out 50% nyquist sampling rate sampling to Lena image, uses the reconstruct of DCT dictionary and the result figure be reconstructed with the present invention;

Fig. 8, when carrying out 50% nyquist sampling rate sampling to House image, uses the result figure that the reconstruct of DCT dictionary is reconstructed with the present invention.

Concrete implementation step

With reference to Fig. 1, specific implementation step of the present invention is as follows:

Step 1. designs the code-disc of digital camera, and the place that code-disc is closed is 0, and the place of opening is 1:

1a) make A be the Toeplitz matrix of a block cyclic shift, wherein each fritter is random Gaussian matrix;

1b) Fourier transform is carried out to matrix A, tries to achieve diagonal matrix: wherein for Fourier transform matrix, for inverse Fourier transform matrix;

1c) use diagonal matrix C _nin diagonal element composition frequency domain response matrix N, inverse Fourier transform is carried out to frequency domain response matrix N, obtains the point spread function designed:

1d) by the coefficient normalization of point spread function h, carry out 0,1 and be similar to, obtain 0,1 alternate code-disc, the place that namely code-disc is closed is 0, and the place of opening is 1.

Step 2. is according to the code-disc of design, and try to achieve the point spread function p in this camera real system, point spread function p is wherein the unit impulse response of camera; By point spread function p, obtain the frequency domain response matrix of camera and the element in frequency domain response matrix M is pulled into diagonal matrix C _m, wherein for Fourier transform matrix.

Step 3. generates Toeplitz observing matrix, carries out low speed sampling to primary signal.

3a) by diagonal matrix C _mcarry out the Toeplitz matrix that Fourier transform obtains block cyclic shift: for inverse Fourier transform matrix;

3b) carry out random down-sampling operation to the Toeplitz matrix B of block cyclic shift, obtain the observing matrix in actual camera system: R=DB, wherein D is random down-sampling matrix, completes the function of low speed sampling in systems in practice.

Step 4., by observing matrix R and original image signal f, obtains measured value: y=Rf;

Step 5. according to real image dimension, original image signal f is divided into non-overlapping copies image fritter, each image fritter is denoted as f respectively _i', i=1,2...n, wherein n is the number of image fritter, and in experiment, image is divided into the image fritter of 16*16, image size is 256*256, image fritter number n=256.

Image fritter Toeplitz observing matrix R observes by step 6., calculates the measured value of each image fritter fi ': y _i'=Rf _i', i=1,2...n.

Step 7. follows the trail of BP restructing algorithm by base, solves the sparse coefficient of corresponding image fritter namely sparse coefficient is obtained by solving following sparse constraint item

$\underset{{\widehat{\mathrm{\α}}}_i}{\min }\left|\right|y_i-\mathrm{RD}{\widehat{\mathrm{\α}}}_i{\left|\right|}_2^2+\mathrm{\λ}\left|\right|{\widehat{\mathrm{\α}}}_i{\left|\right|}_0,$

Wherein, R is observing matrix, y _i, i=1,2...n are that correspondence image block obtains measured value, and D is the sparse dictionary of KSVD dictionary learning method training, and λ is regularization parameter, represent l ₂norm, || || ₀represent l ₀norm.

Step 8. is according to sparse coefficient each image fritter is reconstructed with sparse dictionary D: i=1,2...n.

Step 9. is by all reconstruct small images x _icombine, obtain reconstructed image X '.

Effect of the present invention can be further illustrated by following emulation experiment:

1) experiment condition

Experiment simulation environment: MATLAB2009a, Intel (R) Pentium (R) 1CPU2.4GHz, Window.

Experiment simulation image: the present invention tests 4 width natural images, the size of image is 256 × 256, as shown in Figure 2, wherein, Fig. 2 (a) is Lena image, Fig. 2 (b) is Camera image, and Fig. 2 (c) is Peppers image, and Fig. 2 (d) is House image.

Experimental comparison's method: random Gaussian observing matrix and discrete cosine dictionary DCT.

Experimental result is evaluated: with Y-PSNR PSNR and structural similarity sex index SSIM, Y-PSNR PSNR value is larger, then illustrate that the effect of image reconstruction is better, and structural similarity SSIM is more close to 1, then key diagram picture divides the effect of reconstruction better.

2) experiment content and result

Emulation 1, the reconstruction result figure nyquist sampling rate that the Lena image shown in Fig. 2 (a) carries out 40% sampled with gaussian random observing matrix and the present invention, onesize DCT dictionary is used in restructuring procedure, result as shown in Figure 3, wherein Fig. 3 (a) is for gaussian random observing matrix and DCT dictionary are in conjunction with reconstruction result, the reconstruction result that Fig. 3 (b) is combined with DCT dictionary for Toeplitz observing matrix in the present invention.

Emulation 2, the reconstruction result figure nyquist sampling rate that the Camera image shown in Fig. 2 (b) carries out 40% sampled with gaussian random observing matrix and the present invention, onesize DCT dictionary is used in restructuring procedure, result as shown in Figure 4, wherein Fig. 4 (a) is for gaussian random observing matrix and DCT dictionary are in conjunction with reconstruction result, the reconstruction result that Fig. 4 (b) is combined with DCT dictionary for Toeplitz observing matrix in the present invention.

Emulation 3, the reconstruction result figure nyquist sampling rate that the Peppers image shown in Fig. 2 (c) carries out 40% sampled with gaussian random observing matrix and the present invention, onesize DCT dictionary is used in restructuring procedure, result as shown in Figure 5, wherein Fig. 5 (a) for gaussian random observing matrix and DCT dictionary in conjunction with reconstruction result figure, Fig. 5 (b) for the present invention in the reconstruction result figure that is combined with DCT dictionary of Toeplitz observing matrix.

Emulation 4, the reconstruction result figure of the Nai Kuisi sample rate with gaussian random observing matrix and the present invention, the House image shown in Fig. 2 (d) being carried out to 40%, onesize DCT dictionary is used in restructuring procedure, result as shown in Figure 6, wherein Fig. 6 (a) for gaussian random observing matrix and DCT dictionary in conjunction with reconstruction result figure, Fig. 6 (b) for the present invention in the reconstruction result figure that is combined with DCT dictionary of Toeplitz observing matrix.

Emulation 5, when 50% nyquist sampling rate sampling is carried out to the Lena image shown in 2 (a), use the reconstruct of DCT dictionary and the result figure be reconstructed with the present invention, result as shown in Figure 7, wherein Fig. 7 (a) for DCT dictionary be the reconstruction result figure in the present invention in conjunction with reconstruction result figure, Fig. 7 (b).

Emulation 6, when 50% nyquist sampling rate sampling is carried out to the House image shown in 2 (d), use the reconstruct of DCT dictionary and the result figure be reconstructed with the present invention, result as shown in Figure 8, wherein Fig. 8 (a) for DCT dictionary be the reconstruction result figure in the present invention in conjunction with reconstruction result figure, Fig. 8 (b).

As can be seen from Figure 3, the present invention comparatively uses gaussian random observing matrix reconstructed image to have less blocking effect.

Can find out from the Background Buildings Fig. 4, the present invention has visual effect and image border hold facility more clearly.

As can be seen from Fig. 5 and Fig. 6, the present invention keeps gray scale and ensures that marginal definition has advantage.

As can be seen from Fig. 7 and Fig. 8, visual effect of the present invention is obviously better than additive method.

In order to the advantage of this method is more at large described, Image Reconstruction under different sample rate is emulated, and the average of PSNR and SSIM two numerical index is compared, the result using gaussian random observing matrix and the present invention to reconstruct compares, comparative result is as table 1, the result using the reconstruct of DCT dictionary and the present invention to reconstruct compares, and comparative result is as table 2.

Table 1 uses gaussian random observing matrix and the Average value compare with reconstruction result of the present invention

As can be seen from Table 1, the numerical indication of the present invention under low sampling rate is higher than random Gaussian observing matrix.

Table 2 uses DCT dictionary to reconstruct and reconstructs with the inventive method the contrast carried out

As can be seen from Table 2, compared with the present invention reconstructs with use DCT dictionary, obvious numerical indication is had to promote.

To sum up, the present invention compares the existing image compression method of sampling, evaluate regardless of in numerical index, or in the visual effect of reconstructed image, all there is superiority, can effectively solve in image reconstruction the problem that there is blocking effect, also well can keep the structural information of image, be a kind of feasible effective compression formation method, can well be applied in actual digital camera compression imaging system.

Claims (2)

1. the digital camera based on Toeplitz matrix observation and dictionary learning compresses a formation method, comprises the steps:

(1) design the code-disc of digital camera, the place that code-disc is closed is 0, and the place of opening is 1:

1a) make A be the Toeplitz matrix of a block cyclic shift, wherein each fritter is random Gaussian matrix;

1b) Fourier transform is carried out to matrix A, tries to achieve diagonal matrix: wherein for Fourier transform matrix, for inverse Fourier transform matrix;

1c) use diagonal matrix C _nin diagonal element composition frequency domain response matrix N, inverse Fourier transform is carried out to frequency domain response matrix N, obtains the point spread function designed:

1d) by the coefficient normalization of point spread function h, carry out 0,1 and be similar to, obtain 0,1 alternate code-disc, the place that namely code-disc is closed is 0, and the place of opening is 1;

(2) according to the code-disc of design, try to achieve the point spread function p in this camera real system, obtain the frequency domain response of camera wherein for Fourier transform matrix, the element in matrix M is pulled into diagonal matrix C _m;

(3) by diagonal matrix C _mobtain new Toeplitz matrix: carry out down-sampling operation to Toeplitz matrix B, obtain the observing matrix in actual camera system: R=DB, wherein D is down-sampling matrix, for inverse Fourier transform;

(4) by observing matrix R and original image signal f, measured value is obtained: y=Rf;

(5) original image signal f is divided into non-overlapping copies image fritter, each image fritter is denoted as fi ', i=1,2...n respectively, and wherein n is the number of image fritter;

(6) measured value of each image fritter is calculated: y _i'=Rf _i', i=1,2...n;

(7) follow the trail of BP restructing algorithm by base, solve the sparse coefficient of corresponding image fritter i=1,2...n;

(8) according to sparse coefficient reconstruct each image fritter: i=1,2...n, D _ictit is the dictionary of KSVD dictionary learning method training;

(9) by all reconstruct small images x _icombination obtains reconstructed image X '.

2. the compression of the digital camera based on Toeplitz matrix observation and the dictionary learning formation method according to claims 1, follows the trail of BP restructing algorithm by base wherein described in step (7), solves the sparse coefficient of corresponding image fritter by obtaining following equations, namely

$\underset{{\widehat{\mathrm{\α}}}_i}{min}\left|\right|y_i-{\mathrm{RD}}_{ict}{\widehat{\mathrm{\α}}}_i|{|}_2^2+\mathrm{\λ}|\left|{\widehat{\mathrm{\α}}}_i\right|{|}_0$

Wherein, R is observing matrix, y _i, i=1,2...n are that correspondence image block obtains measured value, D _ictfor the dictionary of KSVD dictionary learning method training, λ is regularization parameter, represent l ₂norm, || || ₀represent l ₀norm.