Reconstruction Algorithms In Compressive Sensing Theory And Their Applications

Compressive Sensing(CS) theory, proposed in 2006, is a new information processing thoery that challenges the dominant Nyquist theory. In CS theory, sampling and compressing processes are completed at the same time, and thus no redundant samples are saved. Researches into CS are in the ascendant. How to reconstruct signals from highly incomplete samples is one of the hot topics.1. Reconstruction algorithms in CS, to be more specific, a series of greedy algorithms and thier applications are researched in this paper. The sparsity of an original signal is unkown, so researchers usually arbitrarily set a number of iteration for OMP, ROMP etc., which leads to reconstruction results not being so accurate. This paper pre-processes the measurements before reconstruction steps on the basis of blocked CS. According to the features of DCT, this paper adopts a mask to manully choose DCT coefficients so as to fix signal sparsity.Reconstruction effectof images is increased significantly.2. Smoothed 0l norm, an approximation to 0l norm, is introduced. CGSL0 algorithm is proposed as an improvement to exsisting SL0 algoithms.It has higher efficiency and better performance as sampling rate increases.3. Data transmission is always with noise, which was always thought "harmful". Owing to the nonlinearity of greedy algorithms, noise plays a positive role in signal reconstruction, in other words, Stochastic Resonance(SR) phenomenon occurs. When noise intensity reaches a certain point, the signal reconstruction effect, measured by mean square error(MSE), is better than that in noiseless situation. A large amount of simulation data shows that signal length and sampling rate, negatively correlated with the best noise intensity, are two most important elements that affect it.