Simultaneous Bayesian compressive sensing and blind deconvolution

The idea of compressive sensing in imaging refers to the reconstruction of an unknown image through a small number of incoherent measurements. Blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown. In this paper, we combine these two problems trying to estimate the unknown sharp image and blur kernel solely through the compressive sensing measurements of a blurred image. We present a novel algorithm for simultaneous image reconstruction, restoration and parameter estimation. Using a hierarchical Bayesian modeling followed by an Expectation-Minimization approach we estimate the unknown image, blur and hyper-parameters of the global distribution. Experimental results on simulated blurred images support the effectiveness of our method. Moreover, real passive millimeter-wave images are used for evaluating the proposed method as well as strengthening its practical aspects.