Bayesian compressive sensing using iterated conditional modes

In this paper we develop a new Bayesian compressive sensing (BCS) decoding algorithm based on iterated conditional modes (ICM) as the inference engine. This approach has the advantage of admitting relatively simple closed-form update rules even for heavy-tailed distributions without resort to conjugate priors and hierarchical models. To demonstrate the simplicity of this approach we derive the ICM update rules for Gaussian, Student´s t, and Levy priors and apply the algorithm to random sparse signals and to the problem of coded aperture superresolution in computational imaging. Simulation results show that the algorithm generally outperforms existing BCS algorithms such as FastLaplace and non-Bayesian sparsity maximization algorithms such as L₁-Magic even in the case of no hyperparameter learning. The BCS-ICM algorithm is highly tunable depending on the nature and amount of prior knowledge. We tune the BCS-ICM algorithm by offline learning of Student´s t parameters for modeling the detail wavelet coefficients for vastly superior performance in the coded aperture superresolution problem.