The Research Of Recovery Algorithms Of Structured Sparse Signal

Sparse signal recovery problem has become a very interesting research topic in the field of signal processing recently. Many researchers have carried on related researches from different aspects and proposed many effective sparse signal recovery algorithms, including structured sparse signal algorithm. This algorithm incorporates structured prior informa-tion of the sparse signals, and thus greatly improves the performance of the algorithm. It has become a new research direction in the field of signal processing. This dissertation will study the structured sparse signal recovery problem, and give some innovations as well as improvements in the sparsity theory and method based on existing sparse signal recovery algorithms.Firstly, we briefly described the basic theory of sparse signal recovery problem. Then, the relevant theories of the classical dictionary learning algorithms and the sparse signal recovery algorithms are introduced, including their main ideas and procedures. Besides, we make a classification of the sparse signal recovery algorithms, and introduce relevant theories of these algorithms. Later, we put forward two kinds of structured sparse signal recovery algorithms about structured sparse problem:one is an initialization method for dictionary learning, the other is sparse Electrocardiogram signals recovery algorithm based on solving a row echelon-like form of system, which improve the performance of the structured sparse signal recovery algorithm. The work of this dissertation is summarized as following:In the second chapter, we utilize the internal structure of signals and incorporate it as a reference into the initialization of the dictionary. Then an new algorithm which improves the original K-SVD algorithm’s performance has been proposed. This algorithm overcomes the limitations of original K-SVD algorithm, which does not consider the prior structure information of signals. Experiments show that the proposed algorithm has a faster convergence speed, lower overall error, and more dictionary atoms that it recovers.Based on the periodic characteristic of ECG signals, in chapter 3, we propose a two-stage recovery algorithm for sparse biosignals in the time domain. In the stage of dictionary learning, the concentration subspaces are found in advance. And then, the dictionary is estimated accurately by exploiting these subspaces. In the stage of sparse signal recovery, we first divide the time points into different layers based on the number of active sources at each time point. Then, by constructing some transformation matrices, these time points form a row echelon-like system. After that, the sources at each layer can be solved out explicitly by corresponding matrix operations. Experiment results show that the proposed method has good performance for sparse ECG signal recovery.Finally, we summarizes the main work of this dissertation, and gives our future researches in the last chapter.