  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.
