Research On Recovery Algorithms And Applications In Compressed Sensing

Based on the signal sparsity structure, integrating sampling and compression, theShannon sampling theorem is broken through by the theory of compressed sensing, whichcan recover the sparse signals exactly from far less samples than those required by theclassical Shannon theorem. Compressed sensing has a wide range of applications thatinclude error correction, image processing, communication engineering, blind source sep-aration, pattern recognition and so on. It promotes the development of the theory andengineering application and has been one of the hottest topics in the feld of signal pro-cessing.The recovery algorithm is an important part of compressed sensing. In compressedsensing model, selecting the appropriate algorithm for diferent signals, recovering theoriginal signal exactly by using as few measurements as possible is the goal. Taking thisas the target and carrying out research on the recovery algorithms, the main contributionsof this paper are as follows.1. Based on the hard thresholding pursuit (HTP), this paper proposes a new greedyalgorithm, aiming at resolving the recovery of sparse signals without the sparsity levelinformation. The algorithm estimates the sparsity level stage by stage, thus it can over-come the difculty caused by the unknown sparsity level information. By using restrictedisometry property (RIP), the sufcient condition for the convergence of the algorithmis presented, and the error between the recovered signal and the original signal is alsogiven. By recovering the synthetic signals and natural images, this paper shows that theproposed algorithm has good performances even without the sparsity level information.2. Based on block mutual coherence, the existing work analyzes the recovery ofsparse signals using block orthogonal matching pursuit (BOMP). This paper presents asufcient condition, based on block RIP, which can ensure to recover the original signalusing BOMP. Also, this paper explains that it is necessary to give the sufcient condition.Redundant blocks may be found in face recognition. This paper proposes an algorithmto solve this problem, and gives a sufcient condition for exactly recovering the supportof unknown sparse vector. Based on multiple measurement vectors (MMV) model, thispaper proposes an algorithm that can simultaneously process many samples. Finally, theefectiveness of the proposed algorithm is shown in the experiment of face recognition.3. The weighted L2,1minimization method is proposed when a part of a sparsesignal’s support is known. By utilizing the correlation of the consecutive frames of signalsequence, this method sees the support of the last frame as prior information, thus, it is possible to recover the original signal using less samples. Based on RIP, the error betweenthe recovered signal and the original signal is presented. In addition, this method directlyregards2D signal as matrix, rather than1D vector, it greatly reduces the running time.The efectiveness of the proposed method is indicated through the recovery of the Larynxsequence.4. Under the additive noise and multiplicative noise, using RIP, this paper aimsat analyzing the theoretical performance of greedy block coordinate descent (GBCD)algorithm. A sufcient condition is presented and an example that satisfes this conditionis also given. The upper bound of this sufcient condition is also analyzed. By giving anexample, this paper shows that GBCD can not exactly recover the support of the originalsignal. Finally, the performance of GBCD is illustrated by experimental results.