Erkmen, Baris I.Goyal, Vivek K.2021-05-052021-05-052018Baris I Erkmen, Vivek K Goyal. "Beyond Thresholding: Analysis and Improvements for Deterministic Parameter Estimation."https://hdl.handle.net/2144/42477Hard-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.en-USArticle0000-0001-8471-7049 (Goyal, Vivek K)598011