{"id":"https://openalex.org/W7133298183","doi":"https://doi.org/10.48550/arxiv.2603.00839","title":"Randomized Tensor Krylov Subspace Methods via Sketched Einstein Product with Applications to Image and Video Restoration","display_name":"Randomized Tensor Krylov Subspace Methods via Sketched Einstein Product with Applications to Image and Video Restoration","publication_year":2026,"publication_date":"2026-02-28","ids":{"openalex":"https://openalex.org/W7133298183","doi":"https://doi.org/10.48550/arxiv.2603.00839"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.00839","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00839","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.00839","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009949456","display_name":"Achraf Badahmane","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Badahmane, Achraf","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009949456"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.37209999561309814,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.37209999561309814,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.20980000495910645,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.11540000140666962,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.6771000027656555},{"id":"https://openalex.org/keywords/orthogonalization","display_name":"Orthogonalization","score":0.5641000270843506},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.551800012588501},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5268999934196472},{"id":"https://openalex.org/keywords/krylov-subspace","display_name":"Krylov subspace","score":0.507099986076355},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.47440001368522644},{"id":"https://openalex.org/keywords/kronecker-product","display_name":"Kronecker product","score":0.4156999886035919},{"id":"https://openalex.org/keywords/cartesian-tensor","display_name":"Cartesian tensor","score":0.40230000019073486},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.3912000060081482}],"concepts":[{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.6771000027656555},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6319000124931335},{"id":"https://openalex.org/C47559304","wikidata":"https://www.wikidata.org/wiki/Q1702189","display_name":"Orthogonalization","level":2,"score":0.5641000270843506},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.551800012588501},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5268999934196472},{"id":"https://openalex.org/C147060835","wikidata":"https://www.wikidata.org/wiki/Q1757151","display_name":"Krylov subspace","level":3,"score":0.507099986076355},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.47440001368522644},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.4156999886035919},{"id":"https://openalex.org/C64835786","wikidata":"https://www.wikidata.org/wiki/Q17004583","display_name":"Cartesian tensor","level":5,"score":0.40230000019073486},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4009999930858612},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39649999141693115},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3912000060081482},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.38749998807907104},{"id":"https://openalex.org/C180623205","wikidata":"https://www.wikidata.org/wiki/Q1268589","display_name":"Outer product","level":3,"score":0.38519999384880066},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.3625999987125397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3456999957561493},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.3434000015258789},{"id":"https://openalex.org/C124007464","wikidata":"https://www.wikidata.org/wiki/Q428091","display_name":"Tensor contraction","level":3,"score":0.3407000005245209},{"id":"https://openalex.org/C1680195","wikidata":"https://www.wikidata.org/wiki/Q2296021","display_name":"Tensor algebra","level":5,"score":0.33570000529289246},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.328900009393692},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3246000111103058},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.32280001044273376},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.3116999864578247},{"id":"https://openalex.org/C2777693668","wikidata":"https://www.wikidata.org/wiki/Q25053743","display_name":"Deblurring","level":5,"score":0.30660000443458557},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.27090001106262207},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.263700008392334},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.2597000002861023}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.00839","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00839","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.00839","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00839","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,48],"develop":[1,61],"a":[2,50,62],"randomized":[3,63],"extension":[4],"of":[5],"tensor":[6,28,39,64,85],"Krylov":[7],"subspace":[8,86],"methods":[9],"based":[10],"on":[11,33],"the":[12],"Einstein":[13,52],"product":[14,54],"for":[15,45,106],"solving":[16,107],"large-scale":[17],"multilinear":[18],"systems":[19],"arising":[20,111],"in":[21,112],"image":[22,114],"and":[23,37,60,93,115],"video":[24,116],"restoration.":[25,117],"The":[26,68,99],"classical":[27],"global":[29,65],"GMRES":[30,73],"method":[31,75,101],"relies":[32],"Frobenius":[34],"inner":[35,53],"products":[36],"full":[38],"orthogonalization,":[40],"which":[41],"become":[42],"computationally":[43],"expensive":[44],"high-dimensional":[46],"problems.":[47],"introduce":[49],"sketched":[51],"constructed":[55],"via":[56],"mode-wise":[57],"random":[58],"projections":[59],"Arnoldi":[66],"process.":[67],"resulting":[69],"Randomized":[70],"Tensor":[71],"Global":[72],"(RTG-GMRES)":[74],"significantly":[76],"reduces":[77],"orthogonalization":[78],"cost":[79],"while":[80],"preserving":[81],"convergence":[82],"properties":[83],"under":[84],"embedding":[87],"assumptions.":[88],"Residual":[89],"bounds,":[90],"perturbation":[91],"analysis":[92],"projected":[94],"Tikhonov":[95],"regularization":[96],"are":[97],"derived.":[98],"proposed":[100],"provides":[102],"an":[103],"efficient":[104],"framework":[105],"ill-posed":[108],"multidimensional":[109],"problems":[110],"color":[113]},"counts_by_year":[],"updated_date":"2026-03-04T07:09:34.246503","created_date":"2026-03-04T00:00:00"}