The Research Of Greedy Matching Pursuit Reconstruction Algorithms For Compressive Sensing

Compressive sensing can sample signal and compress data at the same time when the signal is sparse or can be sparse represented. The data acquisition time and data storage space could be greatly reduced. Reconstruction algorithm is one of the most important parts in compressive sensing. This paper summarized the advantages and disadvantages of the available reconstruction algorithms based on in-depth research, retained the advantages and solved the disadvantages by new methods, then got the new algorithms that have better reconstruction efficiency.Firstly, this paper summarized and introduced the available greedy matching pursuit algorithms. The paper divided all those algorithms into three categories as the basis greedy matching pursuit algorithms, backtracking matching pursuit algorithms and sparsity adaptive matching pursuit algorithms. The paper researched and summarized the advantages and disadvantages of every category for next step of new algorithm research.Secondly, in order to match the sparsity more accurately, the paper presented an improved SAMP algorithm based on regularized backtracking (SAMP-RB). By adapting a regularized backtracking step to SAMP algorithm in each iteration stage, the proposed algorithm can flexibly remove the inappropriate atoms. The experimental results show that SAMP-RB reconstruction algorithm greatly improves SAMP algorithm both in reconstruction quality and computational time. It has better reconstruction efficiency than most of the available matching pursuit algorithms.Finally, the paper presented a new method improved from regularized method. The new method sets an energy threshold for regularization, all subsets that energy in the above of the energy threshold will be selected in one iteration time to avoid the redundancy created by selecting subsets in several iterations. And with the application of the method to regularized orthogonal matching pursuit (ROMP) algorithm and regularized adaptive matching pursuit (RAMP) algorithm, we get two new algorithms called threshold regularized orthogonal matching pursuit (TROMP) algorithm and threshold regularized adaptive matching pursuit (TRAMP) algorithm. The new algorithms TROMP and TRAMP have better reconstruction efficiency than ROMP and RAMP.