Nonlinear regression for signal processing

Alfredo Restrepo

doi:10.1117/12.44332

1 April 1991 Nonlinear regression for signal processing

Alfredo Restrepo

Proceedings Volume 1451, Nonlinear Image Processing II; (1991) https://doi.org/10.1117/12.44332
Event: Electronic Imaging '91, 1991, San Jose, CA, United States

Abstract

A nonlinear regression is a signal that has a specified property (which may be different from linearity) and that optimally approximates a given signal. Such properties are given in the domain of the signal (e.g. time, space) and are called shape constraints. The optimality of the approximation is measured with a semimetric defined on the space of signals under consideration. Finite-length discrete signals are well modeled as point in n-dimensional real space Rn. Thus, for example, a linear regression of a signal is a signal, in the subspace of linear signals, that is closest (usually under the Euclidean metric) to the given signal. Four shape constraints considered in the paper; piecewise constancy, local monotonicity, piecewise linearity and local convex/concavity. They are constraints of smoothness and in this respect, local convex/concavity has the advantage over local monotonicity that a sine wave of small frequency may be locally concave/convex but not locally monotonic. 2D signals defined on quadrille tessellations and on hexagonal tessellations are considered briefly; local monotonicity of degree 3 is defined for 2D signals. A technique for obtaining locally monotonic approximations of 2D signals is presented.

Citation Download Citation

Alfredo Restrepo "Nonlinear regression for signal processing", Proc. SPIE 1451, Nonlinear Image Processing II, (1 April 1991); https://doi.org/10.1117/12.44332

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