Research On Sparse Signal Reconstrcution Algorithms With Noisy Measurement

Compressive Sensing (CS) is an emerging signal sampling theory which has drawn many scholars’attention since being put forward, and the implementation of reconstruction algorithm is its core content. Now researchers are concentrating on the reconstruction algorithms. The present algorithms can be divided into three categories which are named as the class of greedy matching pursuit algorithm, the class of convex optimization algorithm and the class of structure combination. Among them, Greedy matching pursuit algorithm has attracted more interest of many researchers because of its high efficiency and easy implementation. And accordingly, some classical algorithms have already been proposed. However, the greedy algorithm has a rather poor performance when the original signal with large-scale and noisy measurement. This thesis mainly concentrates on the research on greedy algorithms and sparse signal reconstruction algorithms with noisy measurement.The thesis introduces the framework of CS theory and main applications of CS simply, and then the reconstruction algorithm under three different cases are discussed separately. Firstly, we analyze the classical greedy algorithms such as Matching Pursuit (MP) algorithm, Orthogonal Matching Pursuit (OMP) and Regularized Orthogonal Matching Pursuit (ROMP) under the case which with noiseless measurement and a known signal sparsity. On the basis of former study, an improved algorithm called Maximum Correlation Coefficient Regularized Orthogonal Matching Pursuit algorithm (MCC-ROMP) has been proposed. Secondly, this thesis presents an improved algorithm named as Sparsity Adaptive Stage-wise Orthogonal Matching Pursuit (SAStOMP) on the basis of studying the reconstruction algorithms like Stage-wise Orthogonal Matching Pursuit algorithm (StOMP), Sparsity Adaptive Matching Pursuit algorithm (SAMP) and etc under the case which with noiseless measurement and an unknown signal sparsity. Thirdly, We do some research on the Dantzig Selector (DS) and its improved algorithm called Gauss-DS considering the case that with noisy measurement and an unknown signal sparsity. Then the stop conditions of OMP when the OMP algorithm is applied in finding the support of signal correctly under three different kinds of noise are analyzed at the same time. The thesis puts forward a faster and better performance reconstrcution algorithm called Gauss-OMP on the basis of former research. In this thesis, all the algorithms that being studied and improved have been analyzed with simulations in Matlab software. In the simulations, we illustrate the adavantages and disadvantages of the algorithm from two aspects:the running time of algorithm and the percentage of signal exact recovery. In this way, the efficiency of our improved algorithms are proved.