{"id":"https://openalex.org/W4328119932","doi":"https://doi.org/10.3390/e25030535","title":"An Order Reduction Design Framework for Higher-Order Binary Markov Random Fields","display_name":"An Order Reduction Design Framework for Higher-Order Binary Markov Random Fields","publication_year":2023,"publication_date":"2023-03-20","ids":{"openalex":"https://openalex.org/W4328119932","doi":"https://doi.org/10.3390/e25030535","pmid":"https://pubmed.ncbi.nlm.nih.gov/36981423"},"language":"en","primary_location":{"id":"doi:10.3390/e25030535","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25030535","pdf_url":"https://www.mdpi.com/1099-4300/25/3/535/pdf?version=1679318606","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","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/1099-4300/25/3/535/pdf?version=1679318606","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086108034","display_name":"Zhuo Chen","orcid":"https://orcid.org/0000-0002-5314-1435"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhuo Chen","raw_affiliation_strings":["Sichuan University National Key Laboratory of Fundamental Science on Synthetic Vision, Sichuan University, No. 29 Wangjiang Road, Chengdu 610065, China"],"raw_orcid":"https://orcid.org/0000-0002-5314-1435","affiliations":[{"raw_affiliation_string":"Sichuan University National Key Laboratory of Fundamental Science on Synthetic Vision, Sichuan University, No. 29 Wangjiang Road, Chengdu 610065, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087698403","display_name":"Hong\u2010Yu Yang","orcid":"https://orcid.org/0000-0003-2141-5814"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongyu Yang","raw_affiliation_strings":["Sichuan University National Key Laboratory of Fundamental Science on Synthetic Vision, Sichuan University, No. 29 Wangjiang Road, Chengdu 610065, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sichuan University National Key Laboratory of Fundamental Science on Synthetic Vision, Sichuan University, No. 29 Wangjiang Road, Chengdu 610065, China","institution_ids":["https://openalex.org/I24185976"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100394338","display_name":"Yanli Liu","orcid":"https://orcid.org/0000-0001-6734-2601"},"institutions":[{"id":"https://openalex.org/I24185976","display_name":"Sichuan University","ror":"https://ror.org/011ashp19","country_code":"CN","type":"education","lineage":["https://openalex.org/I24185976"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanli Liu","raw_affiliation_strings":["College of Computer Science, Sichuan University, No. 29 Wangjiang Road, Chengdu 610065, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science, Sichuan University, No. 29 Wangjiang Road, Chengdu 610065, China","institution_ids":["https://openalex.org/I24185976"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087698403"],"corresponding_institution_ids":["https://openalex.org/I24185976"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01761156,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"3","first_page":"535","last_page":"535"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.989300012588501,"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/reduction","display_name":"Reduction (mathematics)","score":0.6613948941230774},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6558792591094971},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6126518845558167},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.5443023443222046},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5320421457290649},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.5305761694908142},{"id":"https://openalex.org/keywords/markov-random-field","display_name":"Markov random field","score":0.5123144388198853},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5061447024345398},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.47976693511009216},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4746076464653015},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4716814160346985},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4647274315357208},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4558012783527374},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.4321158230304718},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40476247668266296},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24459007382392883},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.1923733353614807},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1375449001789093},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.07270580530166626},{"id":"https://openalex.org/keywords/image-segmentation","display_name":"Image segmentation","score":0.05874219536781311}],"concepts":[{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6613948941230774},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6558792591094971},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6126518845558167},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.5443023443222046},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5320421457290649},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.5305761694908142},{"id":"https://openalex.org/C2778045648","wikidata":"https://www.wikidata.org/wiki/Q176827","display_name":"Markov random field","level":4,"score":0.5123144388198853},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5061447024345398},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.47976693511009216},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4746076464653015},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4716814160346985},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4647274315357208},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4558012783527374},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.4321158230304718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40476247668266296},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24459007382392883},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.1923733353614807},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1375449001789093},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.07270580530166626},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"score":0.05874219536781311},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e25030535","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25030535","pdf_url":"https://www.mdpi.com/1099-4300/25/3/535/pdf?version=1679318606","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:36981423","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36981423","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":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10048417","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10048417","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10048417/pdf/entropy-25-00535.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:b0c7cd8bda134825a0c405e200f8bd39","is_oa":true,"landing_page_url":"https://doaj.org/article/b0c7cd8bda134825a0c405e200f8bd39","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 25, Iss 3, p 535 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/25/3/535/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e25030535","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy; Volume 25; Issue 3; Pages: 535","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e25030535","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25030535","pdf_url":"https://www.mdpi.com/1099-4300/25/3/535/pdf?version=1679318606","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3053330549","display_name":null,"funder_award_id":"U20A20161","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4328119932.pdf"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W44998981","https://openalex.org/W1774926842","https://openalex.org/W1975605063","https://openalex.org/W2012882037","https://openalex.org/W2074078071","https://openalex.org/W2082165536","https://openalex.org/W2084156819","https://openalex.org/W2101309634","https://openalex.org/W2102424705","https://openalex.org/W2103498186","https://openalex.org/W2110158442","https://openalex.org/W2124558257","https://openalex.org/W2128988466","https://openalex.org/W2130184048","https://openalex.org/W2135165032","https://openalex.org/W2143516773","https://openalex.org/W2152362848","https://openalex.org/W2159565918","https://openalex.org/W2162366888","https://openalex.org/W2164641768","https://openalex.org/W2164918853","https://openalex.org/W2304492655","https://openalex.org/W2732510062","https://openalex.org/W2798768987","https://openalex.org/W2904950256","https://openalex.org/W2964346077","https://openalex.org/W2965581393","https://openalex.org/W3032691033","https://openalex.org/W3035113480","https://openalex.org/W3103545866","https://openalex.org/W3104407133","https://openalex.org/W3119616506","https://openalex.org/W3125883986","https://openalex.org/W3133569444","https://openalex.org/W3162630544","https://openalex.org/W4293103067","https://openalex.org/W4294839247","https://openalex.org/W4309530926","https://openalex.org/W4319591944","https://openalex.org/W4320351999","https://openalex.org/W6677379397","https://openalex.org/W6679258510","https://openalex.org/W6740414469","https://openalex.org/W6778550728"],"related_works":["https://openalex.org/W4233015508","https://openalex.org/W987019958","https://openalex.org/W2099971354","https://openalex.org/W2078379274","https://openalex.org/W2028406636","https://openalex.org/W2114957480","https://openalex.org/W2123898965","https://openalex.org/W2205905062","https://openalex.org/W2120420595","https://openalex.org/W1823779199"],"abstract_inverted_index":{"random":[0],"field":[1],"(RMRF)":[2],"by":[3],"elaborately":[4],"setting":[5],"the":[6,44,52,59,70,74,85,121],"coefficients":[7,60,86],"and":[8,20,61,80,117],"auxiliary":[9,88],"variables":[10,62,89],"of":[11,63,90,105,123],"RMRF.":[12,91],"However,":[13],"designing":[14],"order":[15,35,107],"reduction":[16,36,108],"methods":[17,109],"is":[18,110],"difficult,":[19],"no":[21],"previous":[22],"study":[23,40],"has":[24],"investigated":[25],"this":[26,30,41],"design":[27,37,53,75],"issue.":[28],"In":[29],"paper,":[31],"we":[32,49],"propose":[33],"an":[34],"framework":[38,72],"to":[39],"problem":[42],"for":[43],"first":[45],"time.":[46],"Through":[47],"study,":[48],"find":[50],"that":[51,58],"difficulty":[54,76],"mainly":[55,83],"lies":[56],"in":[57],"RMRF":[64],"must":[65],"be":[66],"set":[67],"simultaneously.":[68],"Therefore,":[69],"proposed":[71],"decomposes":[73],"into":[77],"two":[78],"processes,":[79],"each":[81],"process":[82],"considers":[84],"or":[87],"Some":[92],"valuable":[93],"properties":[94],"are":[95],"also":[96],"proven.":[97],"Based":[98],"on":[99],"our":[100,124],"framework,":[101],"a":[102],"new":[103],"family":[104],"14":[106],"provided.":[111],"Experiments,":[112],"such":[113],"as":[114],"synthetic":[115],"data":[116],"image":[118],"denoising,":[119],"demonstrate":[120],"superiority":[122],"method.":[125]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
