Research Of Block-Sparse Signals Reconstruction Algorithms Based On Structured Compressive Sensing

Compressive Sensing(CS) theory breaks through the limit of traditional Nyquist sampling theorem, it brings a significant change for signal processing technology, and has become a research hotspot at home and abroad in recent years. Based on the traditional compressive sensing, the structured compressive sensing combines the sparsity with the structure information of signals to perform better signal processing results. Reconstruction algorithm is one of the cores of structured compressive sensing, and the block-sparse model is a kind of structure models which is widely used in practical applications. However, there are still a lot of deficiencies in the reconstruction algorithms of block-sparse signals. For this purpose, this thesis focus on the research of block-sparse signals reconstruction algorithms based on structured compressive sensing, the main work is summarized as follows:Aiming at the problems that the Block Orthogonal Matching Pursuit(BOMP) algorithm has no correction ability for the selected blocks and most of existing reconstruction algorithms need the block sparsity of signals as a priori information, firstly, a new algorithm called Forward-Backward Block Pursuit(FBBP) algorithm is proposed. It takes the advantage of backtracking to refine the reliable blocks by forward and backward steps, and iteratively enlarges the block support set by introducing two parameters to close to the block sparsity. Then, the computational complexity of FBBP algorithm is analyzed, and the sufficient condition for accurate reconstruction block-sparse signals is derived. Finally, the experiments show that the FBBP algorithm can reconstruct the block-sparse signals without the prior information of block sparsity and performs better in the aspects of reconstruction precision and the numbers of required measurements than BOMP and BSP.Currently, the reconstruction algorithms of block-sparse signals are almost based on the uniform block-sparse model which has the same size of non-zero blocks and the block sizes are known. However, the sizes of non-zero blocks are usually unequal and unknown in many practical applications. Aiming at this problem, firstly, the lower limit of the numbers of requited measurements for the two different types of block-sparse signals are analyzed. Then, a reconstruction algorithm for the non-uniform block-sparse signals is researched. The algorithm initializes a block size at first, then divides the block-sparse signal uniformly through multiple times with decreasing block size, and gradually eliminate the zero elements among the non-zero blocks via FBBP algorithm to obtain much more precise positions of the non-zero blocks, then the reconstruction error will be reduced. Finally, the simulation experiments show that the proposed algorithm can improve the reconstruction precision of non-uniform block-sparse signal effectively.