TC-CSBP: Compressive sensing for time-correlated data based on belief propagation

Existing compressive sensing techniques mostly consider the sparsity of signals in one dimension. However, a very important case that has rarely been studied is when the signal of interest is time varying and signal coefficients have correlation in time. Our proposed algorithm in this paper is a structure-aware version of the compressive sensing reconstruction via belief propagation proposed by Baron et al. that exploits the time correlation between the signal components and provides the belief propagation algorithm with more accurate initial priors. Numerical simulations show that the belief propagation-based compressive sensing algorithm is able to utilize the side information about signals time correlation and results in enhanced reconstruction performances.