{"paper":{"title":"Generalized Proximal Smoothing for Phase Retrieval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Arjun Rana, Jiawei Miao, Minh Pham, Penghang Yin, Stanley Osher","submitted_at":"2018-03-15T06:22:48Z","abstract_excerpt":"In this paper, we report the development of the generalized proximal smoothing (GPS) algorithm for phase retrieval of noisy data. GPS is a optimization-based algorithm, in which we relax both the Fourier magnitudes and object constraints. We relax the object constraint by introducing the generalized Moreau-Yosida regularization and heat kernel smoothing. We are able to readily handle the associated proximal mapping in the dual variable by using an infimal convolution. We also relax the magnitude constraint into a least squares fidelity term, whose proximal mapping is available. GPS alternative"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05610","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}