We derive the maximum likelihood (ML) estimators for estimating locally monotonic signals embedded in white additive noise, when the noise is assumed to have a density function that is a member of a family of generalized exponential densities with parameter p that includes the Laplacian (p = 1), Gaussian (p = 2) and, as a limiting case, the uniform (p = ∞) densities. The estimators are given by the so-called locally monotonic regression of the noisy signal, a tool of recent introduction in signal processing. The approach that is used in the paper results from a geometric interpretation of the likelihood function of the sample; it takes advantage of the fact that a term in the likelihood function is the p-distance between the vector formed by the data in the given signal (sample) and the vector formed by the elements in the desired signal (estimator). Isotonic regression is a technique used in statistical estimation theory when the data are assumed to obey certain order restrictions. Local monotonicity is a generalization of the concept of isotonicity which is useful for some problems in signal processing.

Date Published: 1 July 1990
PDF: 11 pages
Proc. SPIE 1247, Nonlinear Image Processing, (1 July 1990); doi: 10.1117/12.19600

Published in SPIE Proceedings Vol. 1247:
Nonlinear Image Processing
Edward J. Delp, Editor(s)