Bayesian compressive sensing with polar-distributed low-density sensing matrices

Unlike general random independent identically distributed (i.i.d.) signal, sparse signal in compressive sensing is not i.i.d. and its representation consists of significant coefficients and near-zero coefficients. With consideration of the signal characteristics used in the design method of low density parity check matrix, we propose a design method of low density sensing matrix (LDSM) for the Bayesian compressive sensing framework. Good LDSM is obtained by assuming a two-state mixture Gaussian signal model, by using polar-degree-distributed variable nodes and allocating high degree nodes to the significant coefficients. Simulation results showed that the polar-distributed LDSM results in 35.1% lower mean square error than irregular LDSM which is conventionally optimized in the channel coding problem, even though the noise threshold of the polar-distributed LDSM over BI-AWGN is much lower than the conventionally optimized LDSM.