Fast Algorithms for lp Deconvolution

Abstract

Abstracl-This paper discusses two algorithms for Ip, 1 Q p Q 2, deconvolution. One, iterative reweighted least squares(IRLS), isdiscussed with an eye toward improving its computational efficiency, while the other, residual steepest descent (RSD), is considered in an attempt to improve its convergence properties. In the first case, fast Fourier transforms are used to reduce the number of computations. In the second, a new rescaling procedure which enhances RSD convergence is introduced. The lack of stability of I1, filters, and its implications are discussed. Simple examples are used to illustrate pertinent concepts.