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Compression sensing theory is a signal processing theory framework, which is based on basic subject such as probability statistics theory, matrix analysis theory, functional analysis and topology. For sparse signal or signal which can be sparse represented, signal sampling and signal compression process can be combined into one process, and then the signal reconstruction process is a nonlinear algorithm. The theoretical framework provides a better solution for many practical problems in signal processing. Compared to traditional methods, compressed sensing theory broke through the requirement of Nyquist sampling theorem, it can finish signal processing and reconstruction process by getting a small amount of sample point, so it can reduce the complexity of hardware devices and avoid waste of resources when sampling, transporting and storaging for dealing with redundant redundant information.At present, although the study of compressed sensing theory has made some important achievements, but the study is still stay at preliminary exploration phase, for the three main parts of compressed sensing theory:signal sparse transformation, the design of the observation matrix and the signal reconstruction algorithms, we need still keeping research. As a core part of the compressed sensing theory, signal reconstruction process directly affects the signal reconstruction speed, quality, etc. In this thesis, we analyse the research status of compression sensing theory, introduce compression perception theory framework detailed, and spread the study which revolves around the problem of matching pursuit algorithm research. The main work is as follows:Firstly, we introduce the purpose and significance of compression sensing research and the related research at home and abroad, at the same time, introduce compression perception theory framework detailed, focous on analyzing the details of signal sparse representation, the design of the observation matrix and the signal reconstruction, which are the three main aspects of compression sensing theory.And then analyze the signal reconstruction in detail, for based tracking algorithm, the matching pursuit algorithm, orthogonal matching pursuit algorithm and block orthogonal matching pursuit algorithm, we analyze and compare their basic principle, reconstruct ideas and the main steps of the algorithm flow chart. We take a reconstructed simulation for one dimensional time-domain pulse signal and the2dimensional image, and then analyze the advantages and disadvantages of different algorithms respectively.At last, we introduce Dice coefficient as a new atom matching criteria, apply it to the OMP algorithm, and then we propose a new DOMP algorithm. For the DOMP algorithm, we give a simulation and analysis from the effectiveness and success rate of reconstructing signal, signal reconstruction error and signal reconstruction time, results illustrates the usefulness of DOMP algorithm. The DOMP algorithm and the DStOMP algorithm is applied to the two-dimensional image reconstruction by the relative error for different sampling rates the time and reconstruction of the reconstructed image contrast, analysis of the advantages and disadvantages of the improved algorithm.
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