SCOPE Shrinkage: A Unified Framework for Wavelet Denoising

Statistics > Methodology [Submitted on 17 Jun 2026] Title:SCOPE Shrinkage: A Unified Framework for Wavelet Denoising View PDF HTML (experimental)Abstract:We introduce Symmetric CDF Oriented Probability Enhanced (SCOPE) shrinkage, a unified family of sign-preserving shrinkage rules constructed from centered cumulative distribution functions of symmetric unimodal distributions. The proposed framework generates a broad class of attenuation profiles that interpolate between strong local shrinkage near zero and asymptotically unbiased behavior in the tails. A general formulation is developed that separates scale and shape effects through two interpretable parameters, allowing effective threshold location and transition sharpness to be controlled independently. Under explicit regularity assumptions, structural properties of SCOPE shrinkage are established, including oddness, monotonicity, continuity, contractivity, and a mixture representation that connects the rules to softened thresholding operators. A Bayesian and penalized likelihood interpretation is also developed: SCOPE rules admit even penalty representations that are nondecreasing in coefficient magnitude, and suitable subclasses arise as exact maximum a posteriori estimators under proper symmetric unimodal priors. Representative examples based on logistic, uniform, and Cauchy distributions illustrate how probabilistic shape governs shrinkage behavior. Data driven parameter selection for smooth subclasses is discussed via Stein-type unbiased risk estimation. Oracle calibrated simulation studies on standard Donoho-Johnstone test functions show that SCOPE shrinkage performs competitively with several established wavelet denoising methods, while retaining a high degree of interpretability and structural flexibility. The results highlight centered distribution functions as a natural and versatile design principle for shrinkage in wavelet denoising and related estimation problems. Submission history From: Vijini Lakmini Rathnayake Mudiyanselage [view email][v1] Wed, 17 Jun 2026 20:17:30 UTC (1,928 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.