Blind Compressed Sensing Image Reconstruction Based On Alternating Learning

The most important way for human beings to obtain information is through the visual path.Especially in this age of information revolution,we have more reliance on the way images carry information.Although the rapid development of integrated circuits has greatly improved the speed of image processing,there is an urgent need to resolve the contradiction between the growing demand for big data and relatively lagged image processing methods.The classic Nyquist sampling method has obvious deficiencies for the sampling of high bandwidth signals.1)It is difficult to meet the requirement of fast sampling;2)The sampling cost of the hardware sampling circuit is too high;3)The redundant data generated needs to be compressed after data and then transmitted on the channel,resulting in waste of resources.Since 2006,Compressed Sensing(CS)has been widely used in signal processing because of its maturity and perfection.The theory indicates that if the target signal is sparse in a certain transform domain or the target signal is compressible,the target signal can be accurately reconstructed without adequate sampling.However,the theory of compressed sensing has higher requirements on the a priori of the signal,that is,it needs to have a certain understanding of the sparse coefficients of the signal and the sparse domain.This is exactly the point,which seriously affects the practical application value of the CS theory.Blind Compressed Sensing(BCS)was originally proposed to solve the shortcomings of compressed sensing.This theory combines dictionary learning theory(DL)and CS theory.Dictionary construction refers to constructing an optimal sparse base under sparse representation.It needs to satisfy the conditions for the uniqueness of the coefficients and optimize the solution,and then obtain a more sparse and more accurate representation.Based on the theory of BCS theory,this paper improves and proposes a new type of blind compressed sensing framework,and uses this framework to achieve reconstruction of natural image signals under under-sampling conditions.The scheme is to model the natural image signal as the product of a sparse coefficient matrix S and an over-complete dictionary matrix P.Compared with the classical compressed sensing,the BCS image reconstruction method in this paper simultaneously estimates the sparse coefficient matrix S and the over-complete dictionary matrix P.In order to solve S and P more optimally in the process of alternate iterations,we consider the problem of image reconstruction as a constrained optimization problem,that is,we add regular terms to the optimization process,respectively to two matrices.The solution process is limited in order to avoid over-fitting in the solving of S and P.The Frobenius norm(F-norm)dictionary restriction is to avoid fuzzy reconstruction.In addition,in order to solve the objective function more simply and effectively,we have introduced an auxiliary variable matrix T,which decomposes the original optimization problem into three simpler sub-problems,and adopts a strategy of alternate learning,cycling three sub-problems.Optimal solution.In contrast to the norm and column-norm constraints assumed in most dictionary learning algorithms,the use of penalty and F-norms to constrain the dictionary enables effective attenuation of uncorrelated basis functions.I simulated the BCS reconstruction algorithm and the classical CS algorithm proposed in this paper through the MATLAB2014b software platform,and compared this method with the classic CS reconstruction algorithms OMP,IRLS and CoSaMP.The experimental results show that the BCS proposed in this paper.The scheme can obtain higher reconstruction accuracy than the classical CS image reconstruction method under under-sampling conditions.In the experiment,the PSNR values of the above reconstruction algorithm are calculated respectively.It is found that the PSNR value of the proposed algorithm can be 7dB higher than that of the traditional CS algorithm in the case of under-sampling,and the image is reconstructed visually.The algorithm is heavy.The visual effect of the structured image is clearer,and more details can be highlighted.It can be said that the BCS image reconstruction framework proposed in this paper has better reconstruction performance than the classical compressed sensing scheme.