Beyond thresholding: analysis and improvements for deterministic parameter estimation
Files
First author draft
Date
2018
DOI
Authors
Erkmen, Baris I.
Goyal, Vivek K.
Version
First author draft
OA Version
Citation
Baris I Erkmen, Vivek K Goyal. "Beyond Thresholding: Analysis and Improvements for Deterministic Parameter Estimation."
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 Cramér-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.