Wavelet shrinkage based on the raised cosine prior

2025/07/14 by José J. Reina, Reina, Juliana Marchesi, Alex Rodrigo dos Santos Sousa +1
Computer Science · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2507.10794

openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a Bayesian shrinkage rule to estimate the wavelet coefficients in a nonparametric regression model with Gaussian errors, based on a mixture of a point mass function at zero and a symmetric, zero-centered raised cosine distribution prior. The proposed rule outperformed established shrinkage and thresholding methods in specific scenarios of signal-to-noise ratio and sample size values in conducted simulation studies involving the so-called Donoho and Johnstone test functions. Statistical properties of the rule, such as squared bias, variance, and risks, are analyzed, and two illustrations in real datasets are provided.

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