Research On The Key Technologies Of Compressed Sensing And Its Application In Image Processing

Recently,Compressed sensing(CS) as an exciting, rapidly growing ?eld that has attracted considerable attention in Medical Imaging, Remote Sensing, Image Processing, Military Communications, Wireless Networks And Pattern Recognition. It captures and represents compressible signals at a sampling rate significantly below the Nyquist rate, and come to underlie procedures for sampling and compressing data simultaneously, overcome the large of sample data, and reducing the storage consumption. In this framework, the sampling depend on the content and structure of the signal, rather than depends on the bandwidth as conventional sampling. In this thesis, Develop researches are based on the two important research orientation of compressed sensing—sparse representation and recovery algorithm. New algorithms in sparse representation、measurement design and recovery are proposed,respectively. Specifically, the main research works and innovations as follows:1) A best wavelet packet basis for image processing in sparse representation method is proposed. The quad-tree is introduced to decompose image signal in the algorithm, and the Shannon-entropy is computed. Since Shannon computational formula is semi-additive, an additive function is introduced to simplify the formula, and obtain a best wavelet packet tree. Experiment results show that the proposed method can obtain better sparse representation, and better than single layer wavelet decompression and original compressed sensing.2) By research on the methods that decrease the mutual coherence between a measurement matrix and a basis matrix to optimize measurement matrix, a block-based method is proposed to design measurement matrix. Firstly, the measurement matrix is divided into two blocks. The relationship between the two blocks was obtained by reasoning and proving. Theoretical analysis show that the mutual coherence between the block-based measurement matrix and sparse basis matrix is smaller, to improve and perfect measurement matrix optimization has important practical significance.3) By research on the fundamental of greedy matching pursuit methods, a stepwise subspace pursuit is proposed for sparse signal recovery in compressed sensing. Eliminates useless information from the candidate through threshold processing at first, so reduce time needed to select compatible atoms, and improve the probability to select accurate atoms.