Research Of Image Reconstruction Algorithm Based On Compressed Sensing

The traditional Nyquist sampling theorem is increasingly difficult to meet the data sampling requirement in the information age with data explosion, so there is an urgent need for new sampling methods. In this context, Compressed Sensing theory emerge. It samples signal and compresses the sampled data at the same time, and it breaks through the framework of Nyquist sampling methods. As a a new kind of signal sampling theory, Compressed Sensing has a very nice prospect of research and application. As a core part of the theory of Compressed Sensing, signal reconstruction algorithm will directly determine the success or failure of the practical signal sampling application using the Compressed Sensing theory.This paper focuses on two-dimensional signal (image) reconstruction algorithms based on the theory of Compressed Sensing mainly.Firstly, against the shortcoming of the research on the Compressed Sensing reconstruction algorithms of two-dimensional signal (image), we propose a processing method for image Compressed Sensing reconstruction based on the theory of compressive sensing. Based on the above method, we redesign the typical representation of the three categories of algorithms used for one-dimensional signal which are the convex optimization algorithms based on minimum norm l1, the matching pursuit algorithms and the non-convex optimization algorithms based on minimum norm lp(0<p<1), that is Greedy Basis Pursuit (GBP) algorithm, Orthogonal Matching Pursuit (OMP) algorithm, Subsapce Pursuit (SP) algorithm and Iteratively Reweighted Least Square (IRLS) algorithm, which form some image reconstruction algorithms for image reconstruction of Compressed Sensing. We do the simulation using different images at different sampling rates. The experiments show that the non-convex optimization algorithm based on minimum norm /(0<p<1) represented by Iteratively Reweighted Least Square (IRLS) algorithm has a better reconstruction accuracy than the others, this kind of algorithm is suitable for the case which needs high reconstruction accuracy rather than reconstruction speed; the matching pursuit algorithms represented by Orthogonal Matching Pursuit (OMP) algorithm and Subsapce Pursuit (SP) algorithm has a faster reconstruction speed than the others, this kind of algorithm is suitable for the case which needs high reconstruction speed rather than reconstruction accuracy; the convex optimization algorithm based on minimum norm l1 represented by Greedy Basis Pursuit (GBP) algorithm has no advantage compared to the other algorithms and at the same time it is slow compared to the other algorithms, so this kind of algorithm has little prospect of application in image reconstruction.Secondly, we focus on the Compressive Sampling Matching Pursuit (CoSaMP) algorithm which was used for one-dimensional signal in the matching pursuit algorithms based on the theory of Compressed Sensing. We redesign it to be a Compressed Sensing image reconstruction algorithm for image reconstruction. Taking that the product operation does not maximize the degree of correlation between the atoms in sensing matrix and the residual vector within CoSaMP algorithm into account, while the correlation coefficient can represent the degree of correlation of two vectors better, we propose a MoCoSaMP (Modified CoSaMP) Compressed Sensing image reconstruction algorithm based on correlation coefficient, and we prove the superiority of the new algorithm theoretically. Later, we design simulation at different sample rates for different images. The experiments show that the new proposed algorithm MoCoSaMP improve the quality of the reconstructed image significantly compared to CoSaMP algorithm. So we proved the superiority of the new algorithm actually.