Variational Bayesian compressive blind image deconvolution

We propose a novel variational Bayesian framework to perform simultaneous compressive sensing (CS) image reconstruction and blind deconvolution (BID) as well as estimate all modeling parameters. Furthermore, we show that the proposed framework generalizes the alternating direction method of multipliers which is often utilized to transform a constrained optimization problem into an unconstrained one through the use of the augmented Lagrangian. The proposed framework can be easily adapted to other signal processing applications or particular image and blur priors within the proposed context. In this work, as an example, we employ the following priors to illustrate the significance of the proposed approach: a non-convex l_p quasi-norm based prior for the image, a simultaneous auto-regressive prior for the blur, and an l₁ norm based prior for the transformed coefficients. Experimental results using synthetic images demonstrate the advantages of the proposed algorithm over existing approaches.