Work

The Bayesian SIAC Filter

Year: 2026

Type: article

Abstract: . We propose the Bayesian smoothness-increasing accuracy-conserving (SIAC) filter—a hierarchical Bayesian generalization of the existing deterministic SIAC filter. The SIAC filter is a powerful numerical tool for removing high-frequency noise from data or numerical solutions without degrading accuracy. However, current SIAC methodology is limited to (i) nodal/modal data (noisy direct function values/coefficients of a piecewise polynomial function approximation) and (ii) deterministic point estimates that do not account for uncertainty propagation of input data to the SIAC reconstruction. The proposed Bayesian SIAC filter overcomes these limitations by (i) supporting general (nonnodal) data models and (ii) enabling rigorous uncertainty quantification (UQ), thereby broadening the applicability of SIAC filtering. We also develop structure-exploiting algorithms for efficient maximum a posteriori estimation and Markov chain Monte Carlo sampling, with a focus on linear data models with additive Gaussian noise. Computational experiments demonstrate the effectiveness of the Bayesian SIAC filter across several applications, including signal denoising, image deblurring, and postprocessing of numerical solutions to hyperbolic conservation laws. The results show that the Bayesian approach produces point estimates with accuracy comparable to, and in some cases exceeding, that of the deterministic SIAC filter. In addition, it extends naturally to general data models and provides built-in UQ. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/RomanStuhlmacher/paper-2025-Bayesian-SIAC-Filter and in the supplementary materials ( paper-2025-Bayesian-SIAC-Filter-main.zip [10.1MB]). [Formula: see text]

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/25m1800433

Authors: Jan Glaubitz, Tongtong Li, Jennifer Ryan, Roman Stuhlmacher

Institutions: Linköping University, University of Maryland, Baltimore County, KTH Royal Institute of Technology

Language: English

Topic: Image and Signal Denoising Methods

Subfield: Computer Vision and Pattern Recognition

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Vetenskapsrådet, Office of Naval Research, Air Force Office of Scientific Research

Awards: Institute for Computational and Experimental Research in Mathematics, G1922485206, Revealing hidden features in approximations via convolution kernel multi-resolution analysis, G5256902234, Beyond polynomials: Summation-by-parts operators for general function spaces