Statistical post-processing improves basis pursuit denoising performance

For compressive sensing (CS), we explore the framework of Bayesian linear models to achieve a robust reconstruction performance in the presence of measurement noise. Using a priori statistical knowledge, we develop a two stage method such that the performance of a standard l₁ norm minimization based CS method improves. In the two stage framework, we use a standard basis pursuit denoising (BPDN) method in the first stage for estimating the support set of higher amplitude signal components and then use a linear estimator in the second stage for achieving better CS reconstruction. Through experimental evaluations, we show that the use of the new two stage based algorithm leads to a better CS reconstruction performance than the direct use of the standard BPDN method.