{"id":"https://openalex.org/W4412995579","doi":"https://doi.org/10.3390/axioms14080605","title":"Mitigating the Drawbacks of the L0 Norm and the Total Variation Norm","display_name":"Mitigating the Drawbacks of the L0 Norm and the Total Variation Norm","publication_year":2025,"publication_date":"2025-08-04","ids":{"openalex":"https://openalex.org/W4412995579","doi":"https://doi.org/10.3390/axioms14080605","pmid":"https://pubmed.ncbi.nlm.nih.gov/40855906"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14080605","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080605","pdf_url":"https://www.mdpi.com/2075-1680/14/8/605/pdf?version=1754289751","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/8/605/pdf?version=1754289751","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076268379","display_name":"Gengsheng L. Zeng","orcid":"https://orcid.org/0000-0003-0790-6043"},"institutions":[{"id":"https://openalex.org/I197572798","display_name":"Utah Valley University","ror":"https://ror.org/02rxpxc98","country_code":"US","type":"education","lineage":["https://openalex.org/I197572798"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gengsheng L. Zeng","raw_affiliation_strings":["Department of Computer Science, Utah Valley University, Orem, UT 84058, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Utah Valley University, Orem, UT 84058, USA","institution_ids":["https://openalex.org/I197572798"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076268379"],"corresponding_institution_ids":["https://openalex.org/I197572798"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2099963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"8","first_page":"605","last_page":"605"},"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9998999834060669,"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":0.9990000128746033,"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/norm","display_name":"Norm (philosophy)","score":0.7486737966537476},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6220616698265076},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5629556179046631},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5185856819152832},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.505455493927002},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49612507224082947},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4514918327331543},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43730998039245605},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09925717115402222},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07081344723701477}],"concepts":[{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.7486737966537476},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6220616698265076},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5629556179046631},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5185856819152832},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.505455493927002},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49612507224082947},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4514918327331543},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43730998039245605},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09925717115402222},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07081344723701477},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/axioms14080605","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080605","pdf_url":"https://www.mdpi.com/2075-1680/14/8/605/pdf?version=1754289751","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmid:40855906","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40855906","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":null},{"id":"pmh:oai:doaj.org/article:ff4f0ece1c0d4282a93a3303795c4458","is_oa":true,"landing_page_url":"https://doaj.org/article/ff4f0ece1c0d4282a93a3303795c4458","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 8, p 605 (2025)","raw_type":"article"},{"id":"pmh:oai:europepmc.org:11184989","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/12377048","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms14080605","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080605","pdf_url":"https://www.mdpi.com/2075-1680/14/8/605/pdf?version=1754289751","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412995579.pdf","grobid_xml":"https://content.openalex.org/works/W4412995579.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1593916827","https://openalex.org/W1972150100","https://openalex.org/W1977252496","https://openalex.org/W1978153144","https://openalex.org/W2010473040","https://openalex.org/W2034715615","https://openalex.org/W2038284539","https://openalex.org/W2039472483","https://openalex.org/W2040564415","https://openalex.org/W2044656938","https://openalex.org/W2049819383","https://openalex.org/W2054010646","https://openalex.org/W2059941182","https://openalex.org/W2069629287","https://openalex.org/W2073196514","https://openalex.org/W2104266187","https://openalex.org/W2116627107","https://openalex.org/W2120991191","https://openalex.org/W2133665775","https://openalex.org/W2137620427","https://openalex.org/W2142246791","https://openalex.org/W2145096794","https://openalex.org/W2155942525","https://openalex.org/W2216437871","https://openalex.org/W2621317949","https://openalex.org/W2902564128","https://openalex.org/W2963347434","https://openalex.org/W3040484737","https://openalex.org/W3043164876","https://openalex.org/W3159676427","https://openalex.org/W4234154859","https://openalex.org/W4250955649","https://openalex.org/W4302422232","https://openalex.org/W4366690028","https://openalex.org/W4387823077","https://openalex.org/W4390601009","https://openalex.org/W4392474712","https://openalex.org/W4409290462","https://openalex.org/W6756233496","https://openalex.org/W6861763345"],"related_works":["https://openalex.org/W3034924094","https://openalex.org/W3094954546","https://openalex.org/W1488708774","https://openalex.org/W1982811510","https://openalex.org/W4391100477","https://openalex.org/W2402189625","https://openalex.org/W4327779705","https://openalex.org/W4310560702","https://openalex.org/W1513698804","https://openalex.org/W2083007106"],"abstract_inverted_index":{"In":[0],"compressed":[1],"sensing,":[2],"it":[3],"is":[4,16,34,51,74,122,126,138,182,198],"believed":[5],"that":[6,70,123,162],"the":[7,17,26,57,71,86,91,95,111,114,141,145,163,174,183,189,192,196,204,207,213,218],"<mml:math":[8,27,58,96,115,146,165],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[9,28,59,97,116,147,166],"<mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow>":[10,29,60,98,117,148,167],"<mml:mrow><mml:mn>0</mml:mn></mml:mrow>":[11,30,61,99,118,149,168],"</mml:msub>":[12,31,62,100,119,150,169],"</mml:math>":[13,32,63,101,120,151,170],"norm":[14,33,49,64,73,102,121,152,171],"minimization":[15,50,172],"best":[18],"way":[19],"to":[20,36,78,89,103,139],"enforce":[21,79],"a":[22,39,53,80,105,131,155],"sparse":[23],"solution.":[24],"However,":[25,108],"difficult":[35],"implement":[37],"in":[38,188,210],"gradient-based":[40,132],"iterative":[41],"image":[42],"reconstruction":[43],"algorithm.":[44],"The":[45,177,200],"total":[46],"variation":[47],"(TV)":[48],"considered":[52],"proper":[54],"substitute":[55],"for":[56],"minimization.":[65,176],"This":[66,83],"paper":[67,84,181],"points":[68],"out":[69],"TV":[72,175],"not":[75],"powerful":[76],"enough":[77],"piecewise-constant":[81,106],"image.":[82,107],"uses":[85],"limited-angle":[87],"tomography":[88],"illustrate":[90],"possibility":[92],"of":[93,110,113,144,179,185,191,206,212],"using":[94],"encourage":[104],"one":[109],"drawbacks":[112],"its":[124],"derivative":[125,153],"zero":[127,142],"almost":[128],"everywhere,":[129],"making":[130],"algorithm":[133],"useless.":[134],"Our":[135],"novel":[136],"idea":[137],"replace":[140],"value":[143],"with":[154],"zero-mean":[156],"random":[157],"variable.":[158],"Computer":[159],"simulations":[160],"show":[161],"proposed":[164,208],"outperforms":[173],"novelty":[178],"this":[180],"introduction":[184],"some":[186],"randomness":[187],"gradient":[190,197],"objective":[193],"function":[194],"when":[195],"zero.":[199],"quantitative":[201],"evaluations":[202],"indicate":[203],"improvements":[205],"method":[209],"terms":[211],"structural":[214],"similarity":[215],"(SSIM)":[216],"and":[217],"peak":[219],"signal-to-noise":[220],"ratio":[221],"(PSNR).":[222]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
