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Compressed sensing theory in recent years, the rise of a new sampling theory , while sampling the signal compression, the sampling process and compression process into one , thus breaking the shackles of the traditional Nyquist sampling theorem , This saves a lot of storage, transmission , and computing resources . Firstly, in compressed sensing theory in three key steps to the main line , conducted a systematic review of the theoretical framework of compressed sensing . It includes a sparse representation of the signal , the three parts of the measurement matrix design and signal reconstruction . Then, these three parts were studied. Sparse representation of the signal on signal sparse decomposition of history , and the development of signal sparse decomposition Summary Finally, a comparison and analysis of sparse decomposition algorithm ; measurement matrix design , the design of the measurement matrix classified and analyze the strengths and weaknesses of some commonly used measurement matrix , given the improved design . The reconstructed signal is compressed sensing theory the most important part , this article focuses on the signal reconstruction algorithm , and modified OMP algorithm of the program , described some of the common reconstruction algorithm realization of the principle , and the time the complexity and reconstruction precision of the comparison and analysis , simulation and verification with a two-dimensional image . Detailed study based tracking algorithm and basis pursuit denoising algorithm , and the algorithm has been improved to make it better reconstruction in the case of the signal containing sparse noise ( impulse noise ) , and extended its application range. Finally, the improved algorithm simulation and verification and comparison with the existing algorithms , confirmed that the improved algorithm can effectively improve the effect of remodeling .
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