Multiple description decoding of overcomplete expansions using projections onto convex sets

Abstract

This paper presents a POCS-based algorithm for consistent reconstruction of a signal x/spl isin/R/sup K/ from any subset of quantized coefficients y/spl epsiv/R/sup N/ in an N/spl times/K overcomplete frame expansion y=Fx, N=2K. By choosing the frame operator F to be the concatenation of two K/spl times/K invertible transforms, the projections may be computed in R/sup K/ using only the transforms and their inverses, rather than in the larger space R/sup N/ using the pseudo-inverse as proposed in earlier work. This enables practical reconstructions from overcomplete frame expansions based on wavelet, subband, or lapped transforms of an entire image, which has heretofore not been possible.