CN107016656A - Wavelet Sparse Basis Optimization Method in Image Reconstruction Based on Compressed Sensing - Google Patents

Abstract

The invention relates to a wavelet sparse basis optimization method in image reconstruction based on compressed sensing, that is, the suppression matrix is used to optimize the wavelet sparse basis. First, multi-layer wavelet transform is performed on the original signal data, and the coefficients in the wavelet domain are observed. The coefficients generally show a decreasing trend. Therefore, a suppression matrix is designed to suppress the small coefficients to achieve the purpose of making the coefficients more sparse. This suppression matrix becomes part of the wavelet transform base. The simulation results show that when the sampling rate is in the range of 0.15 to 0.45, the quality of the reconstructed image is improved best, and the peak signal-to-noise ratio is increased by about 0.5dB to 1dB. The texture image reconstruction also has a good effect, which makes up for the shortcomings of the low accuracy of texture image reconstruction based on wavelet transform compressive sensing to a certain extent.

Description

Wavelet Sparse Basis Optimization Method in Image Reconstruction Based on Compressed Sensing

technical field

The invention relates to a wavelet sparse basis optimization method in image reconstruction based on compressed sensing, which is characterized in that the original signal data of the signal is restored and reconstructed with a lower sampling rate to obtain higher-precision original signal data, which is applied to signal compression and Restoration, image processing and computer vision, etc., belong to the field of signal compression transmission and restoration and reconstruction in signal and information processing.

Background technique

The core of compressive sensing is the linear measurement process. Let x(n) be the original signal, the length is N, and y(m) is obtained by multiplying the measurement matrix Φ by the left, and the length is M (M<N). If x(n) is not a sparse signal, the orthogonal sparse transformation will be performed to obtain s(k), which is denoted as x=Ψs, and the measurement process is rewritten as y=Θs, where Θ=ΦΨ(M×N), called traditional Sense matrix, the process is shown in Figure 2.

The signal reconstruction algorithm refers to the process of reconstructing a sparse signal x of length N (M<N) from M measurement vector y. The number N of unknowns in the above equations exceeds the number M of equations, and x(n) cannot be recovered directly from y(m), which can be solved by solving the minimum l ₀ norm problem (1).

But the minimum l ₀ norm problem is an NP-hard problem, which requires exhaustive enumeration of all non-zero values in x permutations are possible and thus cannot be solved. Therefore, the sub-optimal solution algorithm is used to solve the problem, mainly including the minimum l ₁ norm method, matching pursuit series algorithm, iterative threshold method, and the minimum total variation method specially dealing with two-dimensional image problems. At the same time, the measurement matrix Φ satisfies the constraint equidistant condition (RIP condition, Equation 2), and the original signal can be recovered through the above reconstruction algorithm.

The sparse data with a length of 256 is simulated with MATLAB to explore the relationship between data reconstruction accuracy and sparsity. Consider the difference between the reconstructed data and the original data to be lower than a certain threshold as successful data reconstruction, and obtain the reconstruction success rate (input 1000 sets of test data) and the degree of sparsity (m ) relationship (signal length d = 256) as shown in Figure 3. It can be seen from Figure 3 that sufficient sparsity is crucial to improving the accuracy of data reconstruction, so the improvement of data reconstruction in this paper is to create a sparse change base that makes the data more sparse.

Contents of the invention

The technical problem to be solved by the present invention is as follows: Aiming at the insufficient sparsity of the coefficients in the wavelet domain after the existing wavelet transform in the reconstruction of the compressed sensing signal and the problem of low precision after the reconstructed signal, a suppression matrix for the wavelet transform is constructed, Make the wavelet coefficients more sparse. Under the same sampling rate and the same reconstruction conditions, this method can improve the accuracy and signal-to-noise ratio of signal reconstruction to a certain extent.

The technical scheme adopted by the present invention to solve the above-mentioned technical problems is: a wavelet sparse basis optimization method in image reconstruction based on compressed sensing, constructing an easy-to-implement wavelet coefficient suppression matrix, so that the original signal data before the sparse The coefficients become more sparse; then the measured values obtained from the measurement matrix are reconstructed through a reconstruction algorithm to reconstruct the sparse signal, and finally the original signal is reconstructed from the sparse signal through wavelet inverse transform.

Among them, firstly, the original data signal is sparsed by the wavelet sparse basis, and the distribution of coefficients in the wavelet domain is observed. The coefficients generally show a gradually decreasing trend, so the method of suppressing small coefficients can be considered to increase the sparsity of the signal.

Among them, after analyzing the distribution characteristics of wavelet coefficients, a diagonal matrix with the same dimension (n dimension) as the sparse signal is constructed, in which the diagonal element is an arithmetic sequence whose first item is 1 and the tolerance is -1/n, so the wavelet The farther the coefficients are arranged, the smaller the wavelet coefficients are, and the higher the suppression degree is.

Among them, the multiplication of the initial wavelet coefficients and the suppression matrix will obtain more sparse wavelet coefficients, and the measured values obtained from the measurement matrix will be reconstructed through the reconstruction algorithm to obtain the above-mentioned more sparse wavelet coefficients.

Among them, after adding the wavelet coefficient suppression matrix whose diagonal element is an arithmetic sequence, the product of the suppression matrix and the wavelet transform together constitutes a sparse basis, and the product of the inverse matrix of this sparse basis and the sparser wavelet coefficients is The original signal can be recovered and reconstructed.

Principle of the present invention is:

Design a kind of suppression matrix that can suppress small coefficient, make it become the part of sparse transformation basis, the technical scheme that the present invention adopts is:

Use wavelet transform to sparse the original data, as shown in Figure 4 and Figure 5. It can be seen from Figure 4 and Figure 5 that the wavelet transform has greatly sparsed the data, but the sparsity is still not ideal for the reconstruction of compressed sensing data. Observing the coefficient sequence in the wavelet domain of the data signal, it can be seen that the coefficients in the front of the wavelet coefficient sequence are large and the coefficients in the back are small, basically presenting a gradually decreasing trend, so the method of suppressing small coefficients can be considered to improve the sparsity of wavelet coefficients. Therefore, the wavelet coefficient suppression matrix shown in Figure 6 is designed.

The wavelet coefficient suppression matrix in Figure 6 is an n-dimensional diagonal matrix, the diagonal element is an arithmetic sequence whose first item is 1, and the tolerance is -1/n. Multiply this matrix with the coefficients in the previous wavelet transform domain to get A new vector of coefficients, as shown in Figure 7.

It can be seen from Fig. 7 that compared with the coefficient distribution in the initial wavelet domain in Fig. 4, the sparsity of wavelet coefficients has been greatly improved, and the purpose of suppressing small coefficients has been achieved.

The advantage of the present invention compared with prior art is:

(1) the present invention has designed a kind of wavelet coefficient suppression matrix that is easy to realize for the coefficient distribution arrangement characteristic of original data in wavelet domain, and can directly multiply this matrix and wavelet transformation matrix, become the part of sparse variation base, The original wavelet domain coefficients become more sparse, which is beneficial to data reconstruction, and is also easy to analyze theoretically and implement in practice.

(2) The method of the present invention can greatly improve the image reconstruction accuracy. The sampling rate interval is between 0.15 and 0.45, and the reconstruction peak signal-to-noise ratio can be improved by about 0.5dB to 1dB. This sampling rate interval is also an engineering application of compressed sensing image reconstruction. The most commonly used sampling rate range, so the improved technology can be easily put into engineering practice, which is more practical.

(3) Generally speaking, the compression sensing image reconstruction based on wavelet transform of the present invention is relatively poor for the image reconstruction effect of texture detail class, and this improved method has greatly improved the reconstruction accuracy of such high-texture images as fingerprints, making the image The detailed reconstruction ability of the method is enhanced, so to a certain extent, it makes up for the problem of low accuracy of texture image reconstruction by wavelet transform-based compressed sensing in the prior art.

Description of drawings

Fig. 1 is the realization flow chart that the method of the present invention is used for compressed sensing data signal reconstruction;

Fig. 2 is the basic principle block diagram of compressed sensing linear measurement process of the present invention;

Fig. 3 is a relationship diagram between the success rate of compressive sensing signal reconstruction and the number of measured values and the degree of sparsity;

Fig. 4 is original signal data;

Fig. 5 is the sparse data after wavelet transform of original data;

Fig. 6 is the wavelet coefficient suppression matrix constructed in the present invention;

Fig. 7 is the distribution of wavelet coefficients after wavelet transform plus multiplication suppression matrix in the present invention;

Fig. 8 is the relationship curve between the reconstruction Lena image signal-to-noise ratio and the sampling rate before and after the improvement of the present invention;

Fig. 9 is the relationship curve between the reconstructed Fingerprint image signal-to-noise ratio and the sampling rate before and after the improvement of the present invention;

Figure 10 is a comparison of Lena image reconstruction effects before and after the improvement of the present invention;

Fig. 11 is the comparison of the Fingerprint image reconstruction effect before and after the improvement of the present invention;

Figure 12 is a comparison of Lena partial image reconstruction effects before and after the improvement of the present invention;

Fig. 13 is a comparison of the reconstruction effect of the Fingerprint partial image before and after the improvement of the present invention.

detailed description

The present invention will be further described below in conjunction with the detailed description of the accompanying drawings.

It can be seen from the schematic diagram in Figure 2 that the original wavelet sparse transformation base is Ψ ₀ ', assuming that the suppression matrix is w, the final sparse transformation is, wΨ ₀ 'x=s, and wΨ ₀ ' is the improved wavelet sparse transformation basis, that is, Ψ' in the schematic block diagram. The grayscale image of Lena (512*512) and Fingerprint (512*512) is used to do the simulation experiment of image reconstruction through MATLAB respectively. Since the image size is too large, the images are reconstructed in columns, and then spliced into the reconstructed image. full frame image. Since the length of a single data is 512, the size of the suppression matrix is 512*512, the first item of the diagonal element is 1, and the tolerance is an arithmetic sequence of -1/512, so the number of wavelet transform layers of the wavelet transform base is set to 5 layers ( The highest layer with a data length of 512), where the measurement matrix is a Gaussian random matrix, and the reconstruction algorithm uses the Orthogonal Matching Pursuit Algorithm (OMP).

The relationship curves between image reconstruction peak signal-to-noise ratio (PSNR) and sampling rate before and after adding suppression matrix are shown in Fig. 8 and Fig. 9 . It can be seen from Figure 8 and Figure 9 that under the same sampling rate, the peak signal-to-noise ratio of image reconstruction has been improved to a certain extent than before the improvement, and when the sampling rate is between 0.15 and 0.45, this method has Better reconstruction effect, this sampling rate range is also the most commonly used sampling rate range for compressed sensing image reconstruction engineering applications, so it can be put into engineering practice more quickly. When the sampling rate is 0.25, the global and local images of Lena and Fingerprint are used for simulation experiments respectively, and the reconstruction results are shown in Figure 10, Figure 11, Figure 12 and Figure 13.

It can be seen from Figure 10 and Figure 11 that the signal-to-noise ratio and reconstruction accuracy of the image after improvement have been significantly improved compared with those before improvement, especially for fingerprint texture images, it is almost impossible to obtain the texture details of fingerprints before improvement, and it is impossible to Fingerprints are identified, and the texture detail information of the improved fingerprints has been significantly improved, and the fingerprints can be identified. After the global image is simulated and reconstructed, the local area of the image is extracted and reconstructed. The reconstruction effect is shown in Figure 12 and Figure 13.

It can be seen from Figure 12 and Figure 13 that the improved method has greatly improved the reconstruction effect of the local image, the image is smoother and the noise is smaller, and compared with the global image, the accuracy of local image reconstruction with small data and The signal-to-noise ratio is higher, so that the enlarged detail information can basically be clearly presented.

Parts not described in detail in the present invention belong to the known techniques of those skilled in the art.

Those of ordinary skill in the art should recognize that the above embodiments are only used to illustrate the present invention, rather than as a limitation to the present invention, as long as within the scope of the spirit of the present invention, changes to the above embodiments , modification will fall within the scope of the claims of the present invention.

Claims (5)

1. A wavelet sparse basis optimization method in image reconstruction based on compressed sensing, characterized in that: a kind of wavelet coefficient suppression matrix that is easy to implement is constructed, so that the sparse coefficients of the original signal data before the wavelet transform become more sparse; Then the measured values obtained from the measurement matrix are reconstructed through the reconstruction algorithm to reconstruct the sparse signal, and finally the original signal is reconstructed from the sparse signal through wavelet inverse transform. 2. a kind of wavelet sparse basis optimization method based on compressive sensing image reconstruction in claim 1, is characterized in that: first raw data signal is carried out sparse by wavelet sparse basis, observes the coefficient distribution situation in the wavelet domain, coefficient The overall trend is gradually decreasing, so the method of suppressing small coefficients can be considered to increase the sparsity of the signal. 3. a kind of wavelet sparse basis optimization method based on compressive sensing image reconstruction in claim 1 is characterized in that: after analyzing the distribution characteristic of wavelet coefficient, construct a kind of with sparse signal same dimension (n dimension) Diagonal matrix, in which the diagonal element is an arithmetic sequence whose first item is 1 and the tolerance is -1/n, so the farther the wavelet coefficients are arranged, the smaller the wavelet coefficients are, and the higher the suppression degree is. 4. a kind of wavelet sparse basis optimization method based on compressive sensing image reconstruction in claim 1 is characterized in that: original wavelet coefficient and suppression matrix multiplication can obtain more sparse wavelet coefficient, obtain by measurement matrix The measured values of the above-mentioned more sparse wavelet coefficients are obtained through the reconstruction algorithm myopia. 5. a kind of wavelet sparse basis optimization method based on compressive sensing image reconstruction in claim 4 is characterized in that: after adding the wavelet coefficient suppression matrix whose diagonal elements are arithmetic progressions, both suppression matrix and wavelet transform The products together constitute a sparse basis, and the product of the inverse matrix of this sparse basis and the wavelet coefficients can be used to obtain the restored and reconstructed original signal.