Image deconvolution with multi-stage convex relaxation and its perceptual evaluation

This paper proposes a new image deconvolution method using multi-stage convex relaxation, and presents a metric for perceptual evaluation of deconvolution results. Recent work in image deconvolution addresses the deconvolution problem via minimization with non-convex regularization. Since all regularization terms in the objective function are non-convex, this problem can be well modeled and solved by multi-stage convex relaxation. This method, adopted from machine learning, iteratively refines the convex relaxation formulation using concave duality. The newly proposed deconvolution method has outstanding performance in noise removal and artifact control. A new metric, transduced contrast-to-distortion ratio (TCDR), is proposed based on a human vision system (HVS) model that simulates human responses to visual contrasts. It is sensitive to ringing and boundary artifacts, and very efficient to compute. We conduct comprehensive perceptual evaluation of image deconvolution using visual signal-to-noise ratio (VSNR) and TCDR. Experimental results of both synthetic and real data demonstrate that our method indeed improves the visual quality of deconvolution results with low distortions and artifacts.