Diffusion adaptation framework for compressive sensing reconstruction

Compressive sensing (CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from a few measurement data has been intensively studied. In this paper, we propose a novel diffusion adaptation framework for CS reconstruction, where the reconstruction is performed in a distributed network. The data of the measurement matrix are partitioned into small parts and are stored in each node, which assigns the storage load in a decentralized manner. Information diffusion provides the reconstruction ability of each node. Then, a simple and efficient sparsity adaptive diffusion algorithm has been proposed to collaboratively recover the sparse signal over the network. The convergence of the proposed algorithm is analyzed. To further increase the convergence speed, a novel mini-batch based diffusion algorithm is also proposed. Simulation results show that the proposed framework and algorithms can achieve good reconstruction accuracy as well as a much faster convergence speed compared with stand-alone l₀-LMS algorithm for CS.