This article is cited in 5 papers

Unbiased thresholding risk estimate with two threshold values

O. V. Shestakov<sup>abc

a</sup> Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomo- nosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
^b Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
^c Moscow Center for Fundamental and Applied Mathematics, M. V. Lomonosov Moscow State University, 1 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation

Abstract: The problems of noise reduction in signals arise in many application areas. In cases where the signals are not stationary, noise suppression methods based on wavelet transform and thresholding procedures have proven themselves well. These methods are computationally efficient and adapt well to the local features of the signals. The most common types of thresholding are hard and soft thresholding. However, when using hard thresholding, estimates with large variance are obtained, and soft thresholding leads to additional bias. In an attempt to get rid of these shortcomings, various alternative types of thresholding have been proposed in recent years. This paper considers a thresholding procedure with two thresholds which behaves as soft thresholding for small values of wavelet coefficients and as hard thresholding for the large ones. For this type of thresholding, an unbiased estimate of the mean-square risk is constructed and its statistical properties are analyzed. An algorithm for calculating the threshold values that minimizes this estimate is described.

Keywords: wavelets, thresholding, unbiased risk estimate.

Received: 05.08.2022

DOI: 10.14357/19922264220403