Beyond Thresholding: Analysis and Improvements for Deterministic Parameter Estimation
Statistics Theory
2008-01-24 v1 Statistics Theory
Abstract
Hard-threshold estimators are popular in signal processing applications. We provide a detailed study of using hard-threshold estimators for estimating an unknown deterministic signal when additive white Gaussian noise corrupts observations. The analysis, depending heavily on Cram{\'e}r-Rao bounds, motivates piecewise-linear estimation as a simple improvement to hard thresholding. We compare the performance of two piecewise-linear estimators to a hard-threshold estimator. When either piecewise-linear estimator is optimized for the decay rate of the basis coefficients, its performance is better than the best possible with hard thresholding.
Cite
@article{arxiv.0801.3490,
title = {Beyond Thresholding: Analysis and Improvements for Deterministic Parameter Estimation},
author = {Baris I. Erkmen and Vivek K. Goyal},
journal= {arXiv preprint arXiv:0801.3490},
year = {2008}
}
Comments
18 pages, 11 figures