Statistical optimality of locally monotonic regression

Alfredo Restrepo; Alan Conrad Bovik

doi:10.1117/12.19600

1 July 1990 Statistical optimality of locally monotonic regression

Alfredo Restrepo, Alan Conrad Bovik

Proceedings Volume 1247, Nonlinear Image Processing; (1990) https://doi.org/10.1117/12.19600
Event: Electronic Imaging: Advanced Devices and Systems, 1990, Santa Clara, CA, United States

Abstract

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.

Citation Download Citation

Alfredo Restrepo and Alan Conrad Bovik "Statistical optimality of locally monotonic regression", Proc. SPIE 1247, Nonlinear Image Processing, (1 July 1990); https://doi.org/10.1117/12.19600

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