Author :
Sidiropoulos, N.D. ; Baras, J.S. ; Berenstein, C.A.
Author_Institution :
Inst. for Syst. Res., Maryland Univ., College Park, MD, USA
Abstract :
One of the classic problems in the true spirit of nonlinear filtering is that of detecting and estimating edges in noise. The authors pose the following optimization. Given y={y(n)}n=0 N-1∈RN, find a finite-alphabet xˆ={xˆ(n)}n=0N-1∈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)=Σn=1N-1dn(y(n), x(n)) measures the fidelity to the data, and is known as the noise term, and g(x)=Σn=1N-1gn(x(n), x(n-1)) measures the 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), and minimum description length (MDL) on one hand, and nonlinear regression, e.g, VORCA filtering, and digital locally monotonic regression, 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
Keywords :
digital filters; edge detection; filtering theory; noise; nonlinear filters; optimisation; Viterbi-type solution; data fidelity; digital locally monotonic regression; digital nonlinear filtering; edge detection; edge estimation; finite alphabet; hard structural constraint; hard syntactic constraint; minimum description length; noise; noise term; nonlinear regression; optimization; performance; piecewise constant; plateau run-length; smoothness complexity; structurally robust weak continuity; Books; Digital filters; Dynamic programming; Educational institutions; Filtering; Maximum likelihood detection; Noise measurement; Noise robustness; Nonlinear filters; Optical wavelength conversion;
Conference_Titel :
Statistical Signal and Array Processing, 1996. Proceedings., 8th IEEE Signal Processing Workshop on (Cat. No.96TB10004