{"doi":"10.1137/23m1546129","title":"Posterior-Variance–Based Error Quantification for Inverse Problems in Imaging","abstract":".In this work, a method for obtaining pixelwise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal prediction in order to obtain coverage guarantees for the error bounds, without making any assumption on the underlying data distribution. It is generally applicable to Bayesian regularization approaches, independent, e.g., of the concrete choice of the prior. Furthermore, the coverage guarantees can also be obtained in case only approximate sampling from the posterior is possible. With this in particular, the proposed framework is able to incorporate any learned prior in a black-box manner. Guaranteed coverage without assumptions on the underlying distributions is only achievable since the magnitude of the error bounds is, in general, unknown in advance. Nevertheless, experiments with multiple regularization approaches presented in the paper confirm that, in practice, the obtained error bounds are rather tight. For realizing the numerical experiments, a novel primal-dual Langevin algorithm for sampling from nonsmooth distributions is also introduced in this work, showing promising results in practice. While a proof of convergence for this primal-dual algorithm is still open, the theoretical guarantees of the proposed method do not require a guaranteed convergence of the sampling algorithm.KeywordsBayesian imagingconformal predictionuncertainty quantificationerror controllearned priorsinverse problemsMSC codes68U1062F1565C4065C6065J22","journal":"SIAM Journal on Imaging Sciences","year":2024,"id":452880,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":9,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9477,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2024-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":1275080,"name":"Andreas Habring","orcid":"0000-0002-1201-5782","position":1,"is_corresponding":false},{"id":984617,"name":"Martin Höller","orcid":"0000-0002-2895-2375","position":2,"is_corresponding":false},{"id":1018783,"name":"Thomas Pock","orcid":"0000-0001-6120-1058","position":3,"is_corresponding":false},{"id":1275079,"name":"Dominik Narnhofer","orcid":"0000-0002-9293-4112","position":0,"is_corresponding":true}],"reference_count":41,"raw_metadata":null,"created_at":"2026-07-19T02:02:54.415477Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}