Variational Bayesian algorithm for distributed compressive sensing

Distributed compressive sensing (DCS) concerns the reconstruction of multiple sensor signals with reduced numbers of measurements, which exploits both intra- and inter-signal correlations. In this paper, we propose a novel Bayesian DCS algorithm based on variational Bayesian inference. The proposed algorithm decouples the common component, that characterizes inter-signal correlation, from innovation components, that represent intra-signal correlation. Such an operation results in a computational complexity of reconstruction which is linear with the number of signals. The superior performance of the algorithm, in terms of the computing time and reconstruction quality, is demonstrated by numerical simulations in comparison with other existing reconstruction methods.This work is supported by EPSRC Research Grant (EP/K033700/1); the Natural Science Foundation of China (61401018, U1334202); the State Key Laboratory of Rail Traffic Control and Safety (RCS2014ZT08), Beijing Jiaotong University; the Fundamental Research Funds for the Central Universities (2014JBM149); the Key Grant Project of Chinese Ministry of Education (313006); the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education MinistryThis is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/ICC.2015.724909