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Lett."],"published-print":{"date-parts":[[2026,4,15]]},"abstract":"<jats:p>Diffractive neural networks are a promising framework for all-optical processing of visual data, with the potential to drastically reduce the computational burden and energy consumption that is currently associated with running neural networks on digital hardware. Recently, diffractive networks have been applied to various computational imaging tasks. However, while these problems are commonly ill-posed, existing diffractive network designs output only a single reconstruction for each input image, and thus do not inform the user of the inherent uncertainty in the reconstruction. In this work, we explore a passive all-optical diffractive network architecture, together with a dedicated training loss, which allows the network to simultaneously output multiple plausible reconstructions for each input image. We numerically illustrate the efficacy of our method on the tasks of spatial super-resolution and imaging beyond opaque occluders. As we show, the set of diverse outputs generated by the network provides a highly informative visualization of the uncertainty in the reconstruction. Our approach is a first step towards unlocking the full potential of passive all-optical processing in scientific and\/or safety-critical image reconstruction applications.<\/jats:p>","DOI":"10.1364\/ol.583190","type":"journal-article","created":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T02:00:10Z","timestamp":1773280810000},"page":"2012","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["All-optical uncertainty visualization for ill-posed image restoration tasks"],"prefix":"10.1364","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-2621-5286","authenticated-orcid":true,"given":"Matan","family":"Kleiner","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03qryx823","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0525-8054","authenticated-orcid":true,"given":"Tomer","family":"Michaeli","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03qryx823","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,4,2]]},"reference":[{"key":"ol-51-8-2012-R1","doi-asserted-by":"publisher","first-page":"1004","DOI":"10.1126\/science.aat8084","type":"journal-article","volume":"361","author":"Lin","year":"2018","journal-title":"Science"},{"key":"ol-51-8-2012-R2","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1038\/nphoton.2017.93","type":"journal-article","volume":"11","author":"Shen","year":"2017","journal-title":"Nat. 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All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}