Most existing reconstruction algorithms are not robust to the impulsive noise

resulting in a sharp decline in reconstruction performance

so that the entire reconstruction system crashes.A sparse reconstruction algorithm named BINSR is proposed in this paper for the impulsive noise environment.Based on the Bayesian theory

the BINSR algorithm can effectively estimate the support of the sparse signal and the impulse location of impulsive noise.In light of the democracy property of measurements

the MMSE estimate is employed in the BINSR algorithm to achieve effective estimation.And then

combining with robust statistics

a kind of adaptive algorithm termed as ABINSR is proposed in this paper so that it no longer relies on the statistical parameters of signals and impulsive noise.Simulation results demonstrate that the BINSR algorithm can effectively recover sparse signals

greatly improving the reconstruction accuracy in the presence of impulsive noise.Moreover

the ABINSR algorithm is not only robust to the impulsive noise but also effective in the additive white Gaussian environment.