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We prove that GSVT can be obtained by performing the proximal operator of $g$ (denoted as $\\text{Prox}_g(\\cdot)$) on the singular values since $\\text{Prox}_g(\\cdot)$ is monotone when $g$ is lower bounded. If the nonconvex $g$ satisfies some conditions (ma"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.2231","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-12-06T13:08:29Z","cross_cats_sorted":["cs.LG","cs.NA","math.NA"],"title_canon_sha256":"d26785c509f091578b90c663088a6ef34dadb268fc593924e2d26ab0ef28a8ce","abstract_canon_sha256":"ac26aa808bbef62118015232c5f34a524204041315dae7c2231ff30b91ca934a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:57.599528Z","signature_b64":"WxJa8oRCKvyM3ybaopS5O6VCCzsTdUvNU9/GcZ/dtkhPYVf9Dh2HU/L93IjgEZKE5ZbafsB6znj/AULujkbvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"324e2104a32207f692dd60f5de49829e6add6b397ff4044013f049de7aafcf77","last_reissued_at":"2026-05-18T00:14:57.598788Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:57.598788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Singular Value Thresholding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"cs.CV","authors_text":"Canyi Lu, Changbo Zhu, Chunyan Xu, Shuicheng Yan, Zhouchen Lin","submitted_at":"2014-12-06T13:08:29Z","abstract_excerpt":"This work studies the Generalized Singular Value Thresholding (GSVT) operator ${\\text{Prox}}_{g}^{{\\sigma}}(\\cdot)$, \\begin{equation*}\n  {\\text{Prox}}_{g}^{{\\sigma}}(B)=\\arg\\min\\limits_{X}\\sum_{i=1}^{m}g(\\sigma_{i}(X)) + \\frac{1}{2}||X-B||_{F}^{2}, \\end{equation*} associated with a nonconvex function $g$ defined on the singular values of $X$. We prove that GSVT can be obtained by performing the proximal operator of $g$ (denoted as $\\text{Prox}_g(\\cdot)$) on the singular values since $\\text{Prox}_g(\\cdot)$ is monotone when $g$ is lower bounded. 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