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Research on Image Reconstruction Algorithms of Compressive Sensing

Author: ZuoPeng
Tutor: WangAChuan
School: Northeast Forestry University
Course: Applied Computer Technology
Keywords: compressive sensing greedy reconstruction algorithm sparse estimation variablestep size recursive
CLC: TN911.7
Type: Master's thesis
Year: 2013
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Abstract


Compressive sensing is a novel processing method of signals compression and recovery. With the rapid development of modern information technology, traditional sampling compression theory will face two obstacles. On the one hand, the high sampling rate must be satisfied for accurately recovering original signal. On the other hand, some sampling data will be abandoned in the process of signals compression and recovery. In conclusion, the two obstacles will substantially increase information transmission, storage and processing pressure. With the different from traditional methods, the key step of Compressive sensing is the combination of the data sampling and compression, and can exactly recover original signal with less sampling data than nyquist sampling theorem.In this paper, properties of Compressive sensing theorem are firstly comprehensive described. Then analyzing and focusing on the existing reconstruction algorithms. Finally, the improved algorithms are presented for the problems which exist for the SAMP and CoSaMP algorithm. Based on that, the main contributions of this paper are summarized as follows.Firstly, introduces compressed sensing theoretical framework, especially the reconstruction algorithms. Including detailed steps of reconstruction algorithm, performance analysis, etc.Secondly, by researching SAMP algorithm, indicates it has the sparsity adaptive advantages and some other disadvantages. References block matrix operations for SAMP algorithm reconstruction accuracy is not high shortcomings. Finds a reasonable method to make the step in the computing process dynamically shrink and solves the sparsity initial estimate problem. Results demonstrate that the improved algorithm improves the reconstruction accuracy and cuts down computing time compared with the original algorithm.Then, by researching CoSaMP algorithm, indicates it has the noise immunity and high reconstruction accuracy advantages and lack of sparsity adaptive disadvantages. To solve the shortcomings, same as SAMP algorithm, at first it initially estimates the sparse degree, then recovers original signal exactly until meets the termination condition. All of the recursion is under the framework of CoSaMP algorithm, and sparse degree will always increase with the step. Results show that new algorithm with good performance in practical application, meanwhile, with the sparsity adaptive advantage, it also can recover original signal exactly under the noisy condition.Finally, concludes the whole thesis and presents some future work.

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