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Within the Bayesian approach to inverse problems, edge-preservation is often achieved using Markov random field priors based on heavy-tailed distributions. Another strategy, popular in sparse statistical modeling, is the application of hierarchical shrinkage priors. An advantage of this formulation lies in expressing the prior as a conditionally Gaussian distribution depending on global and local hyperparameters which are endowed with heavy-tailed hyperpriors. In this work, we revisit the shrinkage horseshoe prior and introduce its formulation for edge-preserving settings. We discuss a Gibbs sampling framework to solve the resulting hierarchical formulation of the Bayesian inverse problem. In particular, one of the conditional distributions is high-dimensional Gaussian, and the rest are derived in closed form by using a scale mixture representation of the heavy-tailed hyperpriors. Applications from imaging science show that our computational procedure is able to compute sharp edge-preserving posterior point estimates with reduced uncertainty.<\/jats:p>","DOI":"10.1137\/22m1510364","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T10:41:22Z","timestamp":1686307282000},"page":"B337-B365","source":"Crossref","is-referenced-by-count":15,"title":["Horseshoe Priors for Edge-Preserving Linear Bayesian Inversion"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1010-8184","authenticated-orcid":true,"given":"Felipe","family":"Uribe","sequence":"first","affiliation":[{"name":"School of Engineering Science, Lappeenranta-Lahti University of Technology, 53850 Lappeenranta, Finland."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8363-9448","authenticated-orcid":true,"given":"Yiqiu","family":"Dong","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs Lyngby, Denmark."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7333-7216","authenticated-orcid":true,"given":"Per Christian","family":"Hansen","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs Lyngby, Denmark."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,6,9]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1515\/jip-2012-0017"},{"key":"ref2","volume-title":"Computational Uncertainty Quantification for Inverse Problems","author":"Bardsley J. 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