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The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov priors are discretization invariant and can promote sparsity in terms of wavelet coefficients. We propose the randomize-then-optimize method to draw samples from the posterior distribution with Besov priors under a general parameter setting and estimate the modes of the posterior distribution. The performance of the proposed method is studied through numerical experiments of a 1D inpainting problem, a 1D deconvolution problem, and a 2D computed tomography problem. Further, we discuss the influence of the choice of the Besov parameters and the wavelet basis in detail, and we compare the proposed method with the state-of-the-art methods. The numerical results suggest that the proposed method is an effective tool for sampling the posterior distribution equipped with general Besov priors.<\/jats:p>","DOI":"10.1007\/s11222-025-10638-2","type":"journal-article","created":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T08:44:25Z","timestamp":1747989865000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Uncertainty Quantification for Linear Inverse Problems with Besov Prior: A Randomize-Then-Optimize Method"],"prefix":"10.1007","volume":"35","author":[{"given":"Andreas","family":"Horst","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Babak","family":"Maboudi Afkham","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiqiu","family":"Dong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jakob","family":"Lemvig","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,23]]},"reference":[{"issue":"4","key":"10638_CR1","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1111\/1467-9868.00151","volume":"60","author":"F Abramovich","year":"1998","unstructured":"Abramovich, F., Sapatinas, T., Silverman, B.W.: Wavelet thresholding via a bayesian approach. 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