Cooperative Compressive Sampling

Abstract: Compressed Sampling (CS) is a promising technique capable of acquiring and processing data of large sizes efficiently. The CS technique exploits the inherent sparsity present in most real-world signals to achieve this feat. Most real-world signals, for example, sound, image, physical phenomenon etc., are compressible or sparse in nature. This means that a few data samples are sufficient to accurately or closely describe the signal under a suitable representation. The CS technique banks on reconstruction algorithms to recover the original signal upto a desired level of distortion, when required . In this thesis, we design practical CS reconstruction algorithms motivated by cooperation to efficiently recover the original signal.We first consider the case of CS reconstruction at a single node. This problem has been extensively studied in literature. It is observed that for such a scenario there is no single strategy that works best in all problem settings. The performance of CS reconstruction algorithms is heavily influenced by different factors such as sparsity level, signal statistics and the level of undersampling; among others. With this intuition, we propose a general strategy for designing greedy CS reconstruction algorithms. This strategy involves cooperation among several participating CS algorithms in order to achieve better performance. In addition, the general strategy enables the use of off-the-shelf CS reconstruction algorithms and still guarantee theoretical tractability.We next consider the case where CS data samples are available across the nodes of a network. The goal is to estimate a common signal in a distributed setting at the individual nodes. We solve this problem, referred to as distributed sparse learning, through greedy pursuit as well as convex optimization based strategies. Our strategies involve exchange of intermediate estimates among the neighboring nodes in the network. The nodes then refine their estimates over the subsequent iterations to reflect the side information from the neighbors. It is shown that these cooperative strategies lead to fast convergence of the local estimates while achieving better performance results compared to other state-of-the-art distributed sparse learning algorithms.All cooperative CS strategies studied in this thesis are shown to have restricted isometry property (RIP) based reconstruction guarantees. The use of RIP based tools leads to a worst case performance analysis. Hence, we use simulation results to demonstrate the superior performance of the proposed algorithms in typical CS settings.