Research On The Theory And Application Of Compressed Sensing Signal Reconstruction

Compressed sensing theory is the frontier research of recent years,which has been paid highly attention by many research fields.It breaks through the traditional theory of compressed sampling,in which the data are sampled before compressed.And it works through mining the intrinsic structure of the signals-----the signal's sparsity,abandoning a large number of redundant information of the current data,compressing the data needed to be processed into a small sample data by a non-adaptive sampling,and processing the compressed samples directly by using an optimization method to achieve accurate reconstruction of the origin signals.It provides an effective way to solve the problem of mass information transmission,storage and processing.In this dissertation,the theories and methods involved in the reconstruction of compressed sensing signal are studied,which are listed below:1)We deeply investigate the related theory premise of compressed sensing signal reconstruction.Due to the non-homogeneity of the Restricted Isometry Property(RIP)and the Restricted Isometry Property adaptive to the operator B(B-RIP)often conflicts with the measurement amplification,we first give a definition of generalized B-RIP condition for non-orthogonal dictionary.Then under the premise condition,we establish the reconstruction model based on the optimal dual frame,and derive the error bound of the reconstructed signal.Lastly we present an iterative algorithm of the compressed sensing model,and prove the convergence and effectiveness of the algorithm.2)By breaking through the traditional RIP condition theory,we study the problem of compressed sensing reconstruction from the perspective of generalized inverse matrix,and establish the conditions of the(0 1)p??p ? norm reconstruction of compressed sensing signal based on Moore-Penrose generalized inverse.3)For various natural signals varying greatly in terms of geometrical structure and characteristics,which resulting in a good sparse approximation to one type of signals under some sparse operator,but no sparse approximation to other type signals,we proposes an data-driven framework of compressed sensing signal reconstruction based on multi-scale parameterized wavelet frame operator: first of all,we generate the parameterized expression of the sparse wavelet frame operator,and next set up the optimization model based on the parameterized operator,and then learn the sparse operator through the alternative iterative algorithm to get the optimal sparse operator adapt to the input signal,lastly complete the high precision reconstruction.