Diffusion Adaptation Framework for Compressive Sensing Reconstruction (1712.00703v3)

Abstract: 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 few measurement data has been intensively studied. Many reconstruction algorithms have been proposed and shown good reconstruction performance. However, when dealing with large-scale sparse signal reconstruction problem, the storage requirement will be high, and many algorithms also suffer from high computational cost. 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 measurement matrix are partitioned into small parts and are stored in each node, which assigns the storage load in a decentralized manner. The local information interaction provides the reconstruction ability. Then, a simple and efficient gradient-descend based diffusion algorithm has been proposed to collaboratively recover the sparse signal over network. The convergence of the proposed algorithm is analyzed. To further increase the convergence speed, a mini-batch based diffusion algorithm is also proposed. Simulation results show that the proposed algorithms can achieve good reconstruction accuracy as well as fast convergence speed.