Structurally robust weak continuity

N. D. Sidiropoulos, J. S. Baras, C. A. Berenstein

Research output: Contribution to conferencePaperpeer-review

Abstract

We pose the following optimization: Given y = {y(n)}n=0N-1 ε RN, find a finite-alphabet x$+$/ = {x$+$/(n)}n=0N-1 ε AN, that minimizes d(x,y) + g(x) subject to: x satisfies a hard structural (syntactic) constraint, e.g., x is piecewise constant of plateau run-length ≥ M, or locally monotonic of lomo -degree α. Here, d(x,y) = ∑n=0N-1 dn (y(n), x(n)) measures fidelity to the data, and is known as the noise term, and g(x) = ∑n=1N-1 gn(x(n),x(n - 1)) measures smoothness-complexity of the solution. This optimization represents the unification and outgrowth of several digital nonlinear filtering schemes, including, in particular, digital counterparts of Weak Continuity (WC) [6, 7, 2], and Minimum Description Length (MDL) [4] on one hand, and nonlinear regression, e.g., VORCA filtering [11], and Digital Locally Monotonic Regression [10], on the other. It is shown that the proposed optimization admits efficient Viterbi-type solution, and, in terms of performance, combines the best of both worlds.

Original languageEnglish (US)
Pages398-401
Number of pages4
StatePublished - Jan 1 1996
EventProceedings of the 1996 8th IEEE Signal Processing Workshop on Statistical Signal and Array Processing, SSAP'96 - Corfu, Greece
Duration: Jun 24 1996Jun 26 1996

Other

OtherProceedings of the 1996 8th IEEE Signal Processing Workshop on Statistical Signal and Array Processing, SSAP'96
CityCorfu, Greece
Period6/24/966/26/96

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