Model-based and Distributed Compressive Sensing: Algorithms Analyses and Applications

摘要

Compressive sensing (CS) has emerged as a new framework in signal processing which states that one may achieve an exact signal reconstruction from sufficient CS measurements even lower than the well-known Shannon-Nyquist theorem tells us Cost-efficient compressive sensing of large-scale images with quickly reconstructed high-quality results is very challenging We present an algorithm to solve convex optimization via the tree structure sparsity pattern which can be run in the operator to reduce computation cost and maintain good quality especially for large-scale images The feasibility of our method is verified through simulations and comparison with state-of-the-art algorithms On the other hand distributed compressive sensing is a framework considering jointly sparsity within signal ensembles along with multiple measurement vectors (MMVs) The current theoretical bound of performance for MMVs however is derived to be the same with that for single MV (SMV) because the characteristics of signal ensembles are ignored In this work we introduce a new factor called ``Euclidean distances between signals' for the performance analysis of a deterministic signal model under MMVs framework We show that by taking the size of signal ensembles into consideration MMVs indeed exhibit better performance than SMV Although our concept can be broadly applied to CS algorithms with MMVs the case study conducted on a well-known greedy solver called simultaneous orthogonal matching pursuit (SOMP) will be explored in this thesis We show that the performance of SOMP when incorporated with our concept by modifying the steps of support detection and signal estimations will be improved remarkably especially when the Euclidean distances between signals are short The performance of modified SOMP is verified to meet our theoretical prediction In application part we proposed stopping criteria for greedy algorithm based on CS in cooperative spectrum sensing (CSS) We analyze and derive oracle stopping bounds that are independent of prior information such as sparsity for greedy algorithms Simulations are provided to confirm that in compressive cooperative spectrum sensing the proposed stopping criteria for greedy algorithms can remarkably improve detection performance

獎項日期	2017 7月 21
原文	English
監督員	Yung-Fu Fang (Supervisor)