<title>Projection onto the narrow quantization constraint set for postprocessing of scalar quantized images</title>

Abstract

Since the postprocessing of image data using a priori information depends on the constraints imposed on the decoded images, it is important to utilize constraints which are best suited to postprocessing techniques. Among the constraint sets, the quantization constraint set (QCS) is commonly used in various algorithms that are especially based on the theory of projection onto convex sets. In general, the QCS is the closure of the corresponding known quantization region, since such a QCS is the smallest set that is easily predictable at the decoder and always includes the original image before quantization. Our work, however, has revealed that the ordinary QCS is not optimal in the sense of minimum mean square error. Surprisingly, under certain conditions the optimal QCS is always obtained when the boundary of the QCS is narrower than that of the ordinary QCS. In this paper we propose the narrow quantization constraint set (NQCS) as a substitute for the ordinary QCS. We also present mathematical analysis and simulations which demonstrate that the NQCS works better than the ordinary QCS on natural images.