{"id":"https://openalex.org/W2906798660","doi":"https://doi.org/10.1137/19m1237569","title":"Geometry and Symmetry in Short-and-Sparse Deconvolution","display_name":"Geometry and Symmetry in Short-and-Sparse Deconvolution","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2906798660","doi":"https://doi.org/10.1137/19m1237569","mag":"2906798660"},"language":"en","primary_location":{"id":"doi:10.1137/19m1237569","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1237569","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/19m1237569","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028541225","display_name":"Han-Wen Kuo","orcid":"https://orcid.org/0000-0003-2989-5218"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Han-Wen Kuo","raw_affiliation_strings":["Columbia University"],"raw_orcid":"https://orcid.org/0000-0003-2989-5218","affiliations":[{"raw_affiliation_string":"Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100667140","display_name":"Yuqian Zhang","orcid":"https://orcid.org/0000-0001-6080-9125"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuqian Zhang","raw_affiliation_strings":["Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090941231","display_name":"Yenson Lau","orcid":"https://orcid.org/0000-0001-5394-6981"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yenson Lau","raw_affiliation_strings":["cornell University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"cornell University","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019610791","display_name":"John Wright","orcid":"https://orcid.org/0000-0003-2683-4428"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Wright","raw_affiliation_strings":["Columbia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Columbia University","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5028541225"],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.00428518,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"2","issue":"1","first_page":"216","last_page":"245"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/deconvolution","display_name":"Deconvolution","score":0.8057147264480591},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5930772423744202},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5791314840316772},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5624595880508423},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5401235222816467},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5188640356063843},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.44358089566230774},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.387881875038147},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.38571107387542725},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3307974934577942},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3168829083442688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19926249980926514},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09506005048751831},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07875961065292358}],"concepts":[{"id":"https://openalex.org/C174576160","wikidata":"https://www.wikidata.org/wiki/Q1183700","display_name":"Deconvolution","level":2,"score":0.8057147264480591},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5930772423744202},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5791314840316772},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5624595880508423},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5401235222816467},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5188640356063843},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.44358089566230774},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.387881875038147},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38571107387542725},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3307974934577942},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3168829083442688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19926249980926514},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09506005048751831},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07875961065292358},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/19m1237569","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1237569","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1901.00256","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.00256","pdf_url":"https://arxiv.org/pdf/1901.00256","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"mag:2906798660","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1901.00256","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1901.00256","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1901.00256","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1137/19m1237569","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1237569","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.4099999964237213,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G2704916313","display_name":null,"funder_award_id":"IIS 1546411","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3107708848","display_name":null,"funder_award_id":"CCF 1527809","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G984441903","display_name":null,"funder_award_id":"1343282","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W205960364","https://openalex.org/W584962943","https://openalex.org/W589200591","https://openalex.org/W1598281290","https://openalex.org/W1804110266","https://openalex.org/W1941676410","https://openalex.org/W1974618217","https://openalex.org/W1979012241","https://openalex.org/W1987075379","https://openalex.org/W1989291415","https://openalex.org/W1991815226","https://openalex.org/W1992309968","https://openalex.org/W2016902129","https://openalex.org/W2027231794","https://openalex.org/W2032291279","https://openalex.org/W2039665200","https://openalex.org/W2045043668","https://openalex.org/W2062102668","https://openalex.org/W2063978378","https://openalex.org/W2068591523","https://openalex.org/W2086953401","https://openalex.org/W2087054292","https://openalex.org/W2098535678","https://openalex.org/W2100556411","https://openalex.org/W2103913786","https://openalex.org/W2107861471","https://openalex.org/W2108384452","https://openalex.org/W2114018052","https://openalex.org/W2117865218","https://openalex.org/W2121058967","https://openalex.org/W2125857237","https://openalex.org/W2126097106","https://openalex.org/W2130367956","https://openalex.org/W2135238609","https://openalex.org/W2140257560","https://openalex.org/W2140824929","https://openalex.org/W2140867429","https://openalex.org/W2141115311","https://openalex.org/W2143207467","https://openalex.org/W2143570353","https://openalex.org/W2143696095","https://openalex.org/W2150562644","https://openalex.org/W2152623266","https://openalex.org/W2161804069","https://openalex.org/W2162615905","https://openalex.org/W2163636005","https://openalex.org/W2170459977","https://openalex.org/W2171406132","https://openalex.org/W2231009150","https://openalex.org/W2255205876","https://openalex.org/W2516015953","https://openalex.org/W2580665181","https://openalex.org/W2622982709","https://openalex.org/W2745949522","https://openalex.org/W2803992703","https://openalex.org/W2911394281","https://openalex.org/W2962818938","https://openalex.org/W2963507583","https://openalex.org/W2964036861","https://openalex.org/W2965497096","https://openalex.org/W2972345688","https://openalex.org/W3104684837","https://openalex.org/W3104720471"],"related_works":["https://openalex.org/W2963541836","https://openalex.org/W2769885179","https://openalex.org/W3061617046","https://openalex.org/W2753129063","https://openalex.org/W2891377347","https://openalex.org/W3172956674","https://openalex.org/W2951224467","https://openalex.org/W2564550895","https://openalex.org/W3100321248","https://openalex.org/W2753751479","https://openalex.org/W3176725385","https://openalex.org/W2765442055","https://openalex.org/W2107033175","https://openalex.org/W1976793739","https://openalex.org/W1759457718","https://openalex.org/W2259585876","https://openalex.org/W2951870128","https://openalex.org/W2950196470","https://openalex.org/W2085248177","https://openalex.org/W2142455269"],"abstract_inverted_index":{"We":[0,21,65],"study":[1],"the":[2,34,60,85],"short-and-sparse":[3],"(SaS)":[4],"deconvolution":[5,123],"problem":[6],"of":[7,78],"recovering":[8],"a":[9,14,23,42,55,67,76,97,116],"short":[10,36,87],"signal":[11,16,88],"$\\boldsymbol{a}_0$":[12,89],"and":[13,37,94],"sparse":[15,38],"$\\boldsymbol{x}_0$":[17,95],"from":[18],"their":[19],"convolution.":[20],"propose":[22],"method":[24,118],"based":[25],"on":[26,75,111],"nonconvex":[27],"optimization,":[28],"which":[29,46,70],"under":[30],"certain":[31],"conditions":[32],"recovers":[33],"target":[35],"signals,":[39],"up":[40],"to":[41,49],"signed":[43],"shift":[44,91],"symmetry":[45,53],"is":[47],"intrinsic":[48],"this":[50,72,112],"model.":[51],"This":[52],"plays":[54],"central":[56],"role":[57],"in":[58],"shaping":[59],"optimization":[61],"landscape":[62,73],"for":[63],"deconvolution.":[64],"give":[66,115],"regional":[68],"analysis,":[69],"characterizes":[71],"geometrically,":[74],"union":[77],"subspaces.":[79],"Our":[80],"geometric":[81],"characterization":[82],"holds":[83],"when":[84],"length-$p_0$":[86],"has":[90],"coherence":[92],"$\\mu$,":[93],"follows":[96],"random":[98],"sparsity":[99,102],"model":[100],"with":[101,124],"rate":[103],"$\\theta":[104],"\\in":[105],"\\big[\\frac{c_1}{p_0},":[106],"\\frac{c_2}{p_0\\sqrt\\mu":[107],"+":[108],"\\sqrt{p_0}}\\big]\\cdot\\frac{1}{\\log^2p_0}$.":[109],"Based":[110],"geometry,":[113],"we":[114],"provable":[117],"that":[119],"successfully":[120],"solves":[121],"SaS":[122],"high":[125],"probability.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}