Research Of Signal Reconstruction Algorithms Based On Compressed Sensing

The Nyquist sampling theorem requires the sampling frequency must be equal to twice the highest signal frequency at least, but in many cases, the signal bandwidth is so large that the sampling frequency can’t meet the Nyquist sampling theorem. Compressed sensing theory breakthroughs the bondage of Nyquist sampling theorem, it combines data acquisition with data compression as one process, and the sampling frequency of compressed sensing is far lower than the Nyquist sampling frequency. Compressed sensing greatly saves the sampling, transmission and storage costs, and improves the speed and efficiency of information acquisition.Reconstruction algorithms are the key part of compressed sensing, because the accuracy of reconstruction is closely related to the reconstruction algorithms. On the basis of studying the existing reconstruction algorithms depthly, for the shortcomings of reconstruction quality is not high and reconstruction speed is not fast, researches of this paper is as follows:(1) An adaptive matching pursuit algorithm is presented. The new algorithm incorporates backtracking strategy and has the characteristics of sparsity adaptive and is adaptive to adjust the current step size according to the progress of reconstructing and effectively avoids underestimating or overestimating the sparsity of original signal. Moreover, the algorithm can adaptively transform stage, which can not only keep the quality of reconstruction but also improve the speed and efficiency of the algorithm. The experimental results show the effectiveness of the algorithm.(2) A kind of matching pursuit reconstruction algorithm based on adaptive backtracking is presented. The advantages of the algorithm are the adaptive backtracking strategy and adaptive multi-matching principle. Adaptive backtracking strategy improves the reconstruction accuracy and probability of precise reconstruction, and improves the speed of the algorithm at the same time.Adaptive multi-matching principle accelerates the speed of matching atoms and improves the matching accuracy. The experimental results show the effectiveness of the algorithm.(3)A reconstruction algorithm for compressed sensing based on quantum-behaved particle swarm optimization algorithm and lp norm is presented. In this paper, particle swarm optimization algorithm is applied to the compressed sensing reconstruction. As the reconstruction algorithms based on l1-minimizing need more sampled data, this paper transforms the reconstruction model of compressed sensing into the lp-minimization model, and takes lp-minimizing model as the optimization goal of the improved quantum-behaved particle swarm optimization algorithm. Experimental results show that the new algorithm has the advantages of fast convergence, and strong ability of global optimization.