Noniterative reconstruction of band limited signals and coding techniques

Abstract

In this paper we propose linear iterative and noniterative algorithms which can efficiently correct a subset of t samples of a signal, whose values might have been corrupted, possibly due to noise, clipping, or any other reasons. We discuss the applicability of techniques used in error correcting codes to this problem, and the possibility of determining the location of the erroneous samples in oversampled band limited signals. The method borrows ideas from error-correcting codes such as BCH codes, but works in the complex field rather than in a Galois field. This work complements works in reconstruction theory which usually assume that the positions of lost samples or pixels are known, and improves on previously reported nonlinear iterative algorithms.