Study On E2/eq(0<q≤1) Minimization Algorithm For Block Compressed Sensing

Compressed sensing, also known as compressive sensing, is a novel theory which breaks through the sampling limitation based on traditional Nyquis/Shannon sampling theory and makes it into reality that one can efficiently acquire and exactly reconstruct a signal using the prior knowledge that it is sparse or compressible. It has a strong background in application. At present, compressed sensing has been widely used in medical imaging, pattern recognition, compressed imaging system, information transformation.biosensor etc. This thesis. based on compressed sensing, makes a further study on block compressed sensing algorithm. the main works of this thesis are as follows:Chapter one briefly introduces the research background and the recent research situa-tion of compressed sensing, which includes the theories of reconstruction algorithms and its applications.Chapter two mainly presents three basic theories of compressed sensing that is the sparse representation of signals, the design of measurement matrix, reconstruction theories and their relative reconstruction algorithms.Chapter three makes a comprehensive introduction to block compressed sensing theo-ry, including the basic ideal of block-sparsity. the reconstruction theories and their relative algorithms. The theoretical analysis of Block-IRLS algorithm based on l2/lq(0<q<1) min-imization. which mainly contain the error bound estimation and local convergence analysis, is presented next. The theoretical result on error bound estimation indicates that the best s-term approximation and the regularization parameter effectively characterizes the leading influence factor for error control, providing a further theoretical support for error control.Chapter four presents two numerical simulation experiments and their related analysis based on error analysis and algorithm comparisons for the Block-IRLS algorithm. Particu-larly when compared with Block-OMP algorithm. SL20algorithm and SPGL1algorithm, our Block-IRLS algorithm performs best with respect to the success rate of SPGL1algorithm. SL20algorithm. Block-OMP algorithm, and Block-IRLS algorithm are0%,0%,24%,85% respectively.Chapter five is the conclusion part, in which the major findings and implications of the study on block compressed sensing will be made clear. In addition, some tentative suggestions will be provided for further study.