BLIND DECONVOLUTION WHEN NOISE IS SYMMETRIC: EXISTENCE AND EXAMPLES OF SOLUTIONS

STEVEN P. ELLIS

Unit. 42, New York State Psychiatric Institute and Columbia University, 1051 Riverside Dr., New York, NY 10032, U.S.A., e-mail: ellis@neuron.cpmc.columbia.edu

(Received May 12, 2000; revised September 25, 2001)

Abstract. The problem considered is that of identifying two finite dimensional probability distributions G and H from their convolution, F = G ∗ H, when all that is known about them is that H is symmetric. This problem arises in looking for hidden structure in multivariate data, for example. It is shown that one can always find a solution in which G has no nondegenerate symmetric convolution factor. However the solution is not unique in general. Examples of such “completely asymmetric” distributions are given. Existence and examples rather than estimation are the focus of the paper.

Key words and phrases: Image analysis.