Adaptive Regularization Parameter Selection for Discrete Numerical Differentiation of Noisy Signals

Adaptive Regularization Parameter Selection for Discrete Numerical Differentiation of Noisy Signals | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 6 March 2026 V1 Latest version Share on Adaptive Regularization Parameter Selection for Discrete Numerical Differentiation of Noisy Signals Author : Farshad Merrikh-Bayat 0000-0001-6667-2625 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.177282013.35934013/v1 132 views 38 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Estimating derivatives from noisy discrete-time measurements is a classical ill-posed inverse problem. Regularization-based approaches, particularly those inspired by total variation principles, have been widely employed to stabilize the solution. Many existing formulations originate at the functional level, where the optimization problem is posed in the continuous domain. In these formulations, minimization of the functional via the Euler-Lagrange formalism leads to partial differential equations (PDEs), which must then be solved numerically. In contrast, in this paper we propose a fully discrete regularization framework which bypasses the functional-PDE route entirely by formulating the problem directly in a finite-dimensional discrete form. For a fixed value of the regularization parameter, the resulting optimization problem is convex and possesses a closed-form solution that can be obtained via standard linear algebraic operations. The primary contribution of the work is an adaptive strategy for selecting the regularization parameter automatically from the data. We demonstrate that the regularization path contains distinct plateau regions, which reflect the trade-off between noise suppression and signal fidelity. Taking advantage of this behavior, we develop a plateau-guided parameter selection method capable of estimating an optimal or near-optimal regularization level without exhaustive search. Furthermore, the method is extended to a sliding-window setting in which the parameter is updated locally, enabling adaptation to nonstationary noise and time-varying signal features. Numerical experiments demonstrate that the proposed adaptive scheme improves derivative reconstruction accuracy while maintaining computational efficiency, making it suitable for practical large-scale and real-time applications. Supplementary Material File (a_convex_quadratic_formulation_for_numerical_differentiation_of_noisy_signals_via_total_variation_minimization.pdf) Download 368.55 KB Information & Authors Information Version history V1 Version 1 06 March 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords adaptive regularization parameter selection noisy measurement numerical differentiation sliding temporal window total variation Authors Affiliations Farshad Merrikh-Bayat 0000-0001-6667-2625 [email protected] The University of Scranton View all articles by this author Metrics & Citations Metrics Article Usage 132 views 38 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Farshad Merrikh-Bayat. Adaptive Regularization Parameter Selection for Discrete Numerical Differentiation of Noisy Signals. Authorea . 06 March 2026. DOI: https://doi.org/10.22541/au.177282013.35934013/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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