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The Research of Measurement Matrix in Compressed Sensing

Author: WangBiao
Tutor: MaSheXiang
School: Tianjin University of Technology
Course: Signal and Information Processing
Keywords: Compressed Sensing Restricted Isometry Property measurement matrix randomfiltering
CLC: TN911.7
Type: Master's thesis
Year: 2012
Downloads: 191
Quote: 1
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Abstract


With the rapid development of information technology, the need of information in kindsof parts is increasing hardly. The fact that massive need of information gives the heavypressures in sampling, transmitting and storing of signals. How to relieve this pressure andabstract the useful information in the signal effectively is a problem that should be solvedimmediately. The principle of Nyquist ruled the condition of recovering signal accurately, thatis the frequency of sampling can’t be lower than the twice of highest frequency of signal,which is a difficult problem for sampling in signal of high frequency. So a new idea wasraised about building a new framework of describing and processing to sample signal with thefrequency that is far below Nyquist frequency and to recover signal accurately.In recent years, the theory of Compressed Sensing (CS) was proposed by Candes andDonoho to solve the difficulty above. The CS breaks the limit of the Nyquist. The major ideaof the CS is that if the signal is sparse in some transform domain, we can project the highdimension into the low with measurement matrix which is not related to the transform base,and then reconstruct the original signal through solving an optimal problem. The CS includessparse transformation, projection and measurement and signal reconstruction. But it is still notmature, so there are a lot of experts and scholars studying in different parts of CS.This paper makes the study mainly on signal measurement and did some works.Hereanalyzed the idea and complement process of CS, and analyzed the Restricted IsometryProperty (RIP) generally which the measurement matrix must be satisfied with. We proposedthe method of improving the Gaussian random measurement matrix to build a newmeasurement matrix which has better performance than traditional ones. This paper broughtthe random filtering into CS to solve the problems in processing of real-time signal or vastdata assemble which CS is confronted with and get the better results.

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