Compressed Sensing Based Super-resolution Theory And Technology Research

In the field of communication, the amount of signal need to be processed is becoming more and more, the signal itself is also more and more complicated. In traditional signal processing, signal sampling is limited by the Nyquist sampling rate, unable to cope with this situation. And compressed sensing breakthrough the Nyquist sampling rate, by using the sparse property of signal, it can do signal sampling with a very low sampling rate, and obtain accurate reconstruction, however. In recent years, many scholars combined compressed sensing and super-resolution technology, hope to take advantage of compressed sensing’s characteristic of low sampling rate, while at the same time obtain signal estimation and recovery algorithm with super-resolution.This thesis analyzes classic compressed sensing algorithms, traditional super-resolution algorithms and super-resolution algorithms based on compressed sensing. Classic compressed sensing algorithms, such as Orthogonal Matching Pursuit(OMP), Basis Pursuit(BP), Iterative Hard Thresholding(IHT), Iterative reweighted Least Square(IRLS), Sparse Bayesian Learning(SBL), all of them try to reconstruct signal accurate, with a small amount of samples. Traditional super-resolution algorithm, such as MUSIC and ESPRIT, are based on subspace, with sufficient samples, they can achieve very high estimate accuracy. Super-resolution algorithm based on compressed sensing, such as the recent SIHT, OGSBI, DicRef CS, SDP algorithm, only need a small amount of samples, while still obtain accurate reconstruction.Based on the analysis of the above algorithm, and consider that existing super-resolution algorithms based on compressed sensing have the so-called basis mis-match problem, their performance is not ideal. In this thesis, in noiseless and noisy cases respectively, an iterative reweighted jointly estimation and recovery algorithm based on compressed sensing with super-resolution is proposed, which can solve the basis mis-match problem better. And put forward an effective strategy to select regularization parameter in noisy cases dynamically. Simulation experiments for spectral estimation and DOA estimation problem show that the proposed iterative reweighted jointly estimation and recovery algorithm, compared with the existing algorithms based on compressed sensing, has obvious advantages, which to a large extent overcome basis mis-match problem. And it has better anti-noise performance, meanwhile can obtain a performance of super-resolution.