A Perturbation Analysis Of (?)_q(0<q≤1)Minimization For Block-spare Signal Data

With the development of information technology, people’s demand for information is constantly increasing, and thus brings great pressure to the sampling storage and transmission for signal data. In recent years, compressed sensing is proposed, which not only greatly reduces the sampling costs, but also reduces the cost of storage and transmission of signal data. Based on compressed sensing, this thesis makes a study on the complete perturbation theories of ?_q（0 <q≤1） minimization for block-sparse signal data, and the main works of this thesis are as follows:Chapter one introduces the research background and recent research situation of compressed sensing and block compressed sensing, and summarizes the main works and organization structure of this thesis.Chapter two presents the theory of compressed sensing from the three core theories that are the sparse representation of signal data, the design of measurement matrix, and the reconstruction theories.Chapter three introduces the block-sparse signal data and the reconstruction theories of them, and concentrates on studying the completely perturbed mixed ?₂/ ?_q（0 < q ≤ 1）minimization method. We not only establish a sufficient condition but also obtain an error upper bound which is proportional to and controlled by the best k-block approximation and the total noise. In addition, we improve the obtained results for the case of q = 1, and the results show that not only a better sufficient condition is achieved, but also a tighter error upper bound is obtained.Chapter four gives the Block-IRLS methodology in the case of complete perturbation,and based on it some numerical experiments are conducted to support the validation of our theoretical results. By comparing with other typical algorithms, numerical experiments demonstrate that Block-IRLS methodology has better ability to process signal data in the completely perturbed case. In addition, the experiments also indicate that the block structure plays an important role for processing block-sparse signal data in the case of complete perturbation.Chapter five summaries the works of this thesis, and provides some tentative suggestions for further study.