{"id":"https://openalex.org/W3183911236","doi":"https://doi.org/10.1109/tsp.2021.3098936","title":"Deep Scattering Network With Fractional Wavelet Transform","display_name":"Deep Scattering Network With Fractional Wavelet Transform","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3183911236","doi":"https://doi.org/10.1109/tsp.2021.3098936","mag":"3183911236"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2021.3098936","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3098936","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032530028","display_name":"Jun Shi","orcid":"https://orcid.org/0000-0001-6194-4433"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Shi","raw_affiliation_strings":["Communication Research Center, Harbin Institute of Technology, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Communication Research Center, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101460721","display_name":"Yanan Zhao","orcid":"https://orcid.org/0000-0002-2761-696X"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanan Zhao","raw_affiliation_strings":["Communication Research Center, Harbin Institute of Technology, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Communication Research Center, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100389005","display_name":"Wei Xiang","orcid":"https://orcid.org/0000-0002-0608-065X"},"institutions":[{"id":"https://openalex.org/I196829312","display_name":"La Trobe University","ror":"https://ror.org/01rxfrp27","country_code":"AU","type":"education","lineage":["https://openalex.org/I196829312"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Wei Xiang","raw_affiliation_strings":["School of Engineering and Mathematical Sciences, La Trobe University, Melbourne, VIC, Australia"],"raw_orcid":"https://orcid.org/0000-0002-0608-065X","affiliations":[{"raw_affiliation_string":"School of Engineering and Mathematical Sciences, La Trobe University, Melbourne, VIC, Australia","institution_ids":["https://openalex.org/I196829312"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014013504","display_name":"Vishal Monga","orcid":"https://orcid.org/0000-0002-5100-2263"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vishal Monga","raw_affiliation_strings":["Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, USA"],"raw_orcid":"https://orcid.org/0000-0002-5100-2263","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112545348","display_name":"Xiaoping Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoping Liu","raw_affiliation_strings":["School of Information and Electronics, Beijing Institute of Technology and the Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-6194-4433","affiliations":[{"raw_affiliation_string":"School of Information and Electronics, Beijing Institute of Technology and the Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067803447","display_name":"Ran Tao","orcid":"https://orcid.org/0000-0002-5243-7189"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ran Tao","raw_affiliation_strings":["School of Information and Electronics, Beijing Institute of Technology and the Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-5243-7189","affiliations":[{"raw_affiliation_string":"School of Information and Electronics, Beijing Institute of Technology and the Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.2538,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.93258051,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"69","issue":null,"first_page":"4740","last_page":"4757"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":1.0,"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":1.0,"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/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9968000054359436,"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/wavelet","display_name":"Wavelet","score":0.6981931924819946},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.6606623530387878},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5679628252983093},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5491809248924255},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.5482781529426575},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.5253053307533264},{"id":"https://openalex.org/keywords/stationary-wavelet-transform","display_name":"Stationary wavelet transform","score":0.4718865156173706},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43702277541160583},{"id":"https://openalex.org/keywords/continuous-wavelet-transform","display_name":"Continuous wavelet transform","score":0.42040857672691345},{"id":"https://openalex.org/keywords/harmonic-wavelet-transform","display_name":"Harmonic wavelet transform","score":0.41026219725608826},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.40032804012298584},{"id":"https://openalex.org/keywords/wavelet-packet-decomposition","display_name":"Wavelet packet decomposition","score":0.33402764797210693},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.3289772868156433}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6981931924819946},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.6606623530387878},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5679628252983093},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5491809248924255},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.5482781529426575},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5253053307533264},{"id":"https://openalex.org/C73339587","wikidata":"https://www.wikidata.org/wiki/Q1375942","display_name":"Stationary wavelet transform","level":5,"score":0.4718865156173706},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43702277541160583},{"id":"https://openalex.org/C95722684","wikidata":"https://www.wikidata.org/wiki/Q2622756","display_name":"Continuous wavelet transform","level":5,"score":0.42040857672691345},{"id":"https://openalex.org/C1109138","wikidata":"https://www.wikidata.org/wiki/Q3280930","display_name":"Harmonic wavelet transform","level":5,"score":0.41026219725608826},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.40032804012298584},{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.33402764797210693},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.3289772868156433}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2021.3098936","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3098936","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3403064617","display_name":null,"funder_award_id":"QC2018078","funder_id":"https://openalex.org/F4320323085","funder_display_name":"Natural Science Foundation of Heilongjiang Province"},{"id":"https://openalex.org/G4391318493","display_name":null,"funder_award_id":"HIT.NSRIF.2019027","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G4417359500","display_name":null,"funder_award_id":"U1833203","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4639895821","display_name":null,"funder_award_id":"61421001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7161545915","display_name":"\u57fa\u4e8e\u7ebf\u6027\u6b63\u5219\u53d8\u6362\u7684\u4fe1\u53f7\u91c7\u6837\u7406\u8bba\u4e0e\u91cd\u6784\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61871153","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"},{"id":"https://openalex.org/F4320323085","display_name":"Natural Science Foundation of Heilongjiang Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W284396425","https://openalex.org/W606473257","https://openalex.org/W1495573900","https://openalex.org/W1545302199","https://openalex.org/W1549358575","https://openalex.org/W1975142646","https://openalex.org/W1981166187","https://openalex.org/W1994906459","https://openalex.org/W2050697133","https://openalex.org/W2054575057","https://openalex.org/W2059511347","https://openalex.org/W2072072671","https://openalex.org/W2075314800","https://openalex.org/W2093231248","https://openalex.org/W2100619198","https://openalex.org/W2102116272","https://openalex.org/W2110063971","https://openalex.org/W2112796928","https://openalex.org/W2117752214","https://openalex.org/W2119943055","https://openalex.org/W2145080587","https://openalex.org/W2163605009","https://openalex.org/W2163782669","https://openalex.org/W2253210145","https://openalex.org/W2261689926","https://openalex.org/W2406696299","https://openalex.org/W2479221532","https://openalex.org/W2558748708","https://openalex.org/W2589910641","https://openalex.org/W2652471884","https://openalex.org/W2763292971","https://openalex.org/W2792680145","https://openalex.org/W2810555899","https://openalex.org/W2884013187","https://openalex.org/W2892340991","https://openalex.org/W2892801568","https://openalex.org/W2901461790","https://openalex.org/W2922255081","https://openalex.org/W2941724526","https://openalex.org/W2945837706","https://openalex.org/W2957558419","https://openalex.org/W2959195885","https://openalex.org/W2963013747","https://openalex.org/W2963747696","https://openalex.org/W2964336243","https://openalex.org/W2970958999","https://openalex.org/W2971620842","https://openalex.org/W2988187203","https://openalex.org/W2998838085","https://openalex.org/W3008725350","https://openalex.org/W3013102563","https://openalex.org/W3090460073","https://openalex.org/W3102380997","https://openalex.org/W3103167764","https://openalex.org/W3103699521","https://openalex.org/W3105204625","https://openalex.org/W3106050203","https://openalex.org/W4239440589","https://openalex.org/W6632978964","https://openalex.org/W6684191040","https://openalex.org/W6748210201"],"related_works":["https://openalex.org/W2085792030","https://openalex.org/W1986475093","https://openalex.org/W2144408025","https://openalex.org/W1967182499","https://openalex.org/W1588899229","https://openalex.org/W1917032666","https://openalex.org/W2205192157","https://openalex.org/W2156522110","https://openalex.org/W2050815068","https://openalex.org/W2576267406"],"abstract_inverted_index":{"Deep":[0],"convolutional":[1],"neural":[2],"networks":[3],"(DCNNs)":[4],"have":[5],"recently":[6],"emerged":[7],"as":[8,141,206,208],"a":[9,26,44,93,142,175,199],"powerful":[10],"tool":[11],"to":[12,51,127],"deliver":[13],"breakthrough":[14],"performances":[15],"in":[16,86,116],"various":[17],"image":[18,87,101,106],"analysis":[19],"and":[20,30,80,149,186],"processing":[21],"applications.":[22,211],"However,":[23],"DCNNs":[24,79],"lack":[25],"strong":[27],"theoretical":[28,213],"foundation":[29],"require":[31],"massive":[32],"amounts":[33],"of":[34,46,60,78,123,144,191,202],"training":[35],"data.":[36],"More":[37],"recently,":[38],"the":[39,57,83,117,132,162,170,179,203],"deep":[40],"scattering":[41,165],"network":[42],"(DSN),":[43],"variant":[45],"DCNNs,":[47,61],"has":[48],"been":[49],"proposed":[50],"address":[52],"these":[53],"issues.":[54],"DSNs":[55,90],"inherit":[56],"hierarchical":[58],"structure":[59,177],"but":[62,103],"replace":[63],"data-driven":[64],"linear":[65,113,145],"filters":[66,115,148],"with":[67],"predefined":[68],"fixed":[69],"multi-scale":[70,147],"wavelet":[71,134,164,184],"filters,":[72],"which":[73,137],"facilitate":[74],"an":[75],"in-depth":[76],"understanding":[77],"also":[81],"offer":[82],"state-of-the-art":[84],"performance":[85],"classification.":[88],"Unfortunately,":[89],"suffer":[91],"from":[92],"major":[94],"drawback:":[95],"they":[96],"are":[97,111,195,215],"suitable":[98],"for":[99,155,178],"stationary":[100],"textures":[102],"not":[104],"non-stationary":[105,156],"textures,":[107],"since":[108],"2D":[109],"wavelets":[110],"intrinsically":[112],"translation-invariant":[114],"Fourier":[118],"transform":[119,135,166],"domain.":[120],"The":[121,212],"objective":[122],"this":[124,129,192],"paper":[125],"is":[126],"overcome":[128],"drawback":[130],"using":[131],"fractional":[133,163,183],"(FRWT)":[136],"can":[138],"be":[139,152],"viewed":[140],"bank":[143],"translation-variant":[146],"thus":[150],"may":[151],"well":[153,207],"suited":[154],"texture":[157],"analysis.":[158],"We":[159],"first":[160],"propose":[161],"(FRWST)":[167],"based":[168],"upon":[169],"FRWT.":[171],"Then,":[172],"we":[173],"present":[174],"generalized":[176,193,204],"DSN":[180,194,205],"by":[181,198],"cascading":[182],"convolutions":[185],"modulus":[187],"operators.":[188],"Basic":[189],"properties":[190],"derived,":[196],"followed":[197],"fast":[200],"implementation":[201],"their":[209],"practical":[210],"derivations":[214],"validated":[216],"via":[217],"computer":[218],"simulations.":[219]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":3}],"updated_date":"2026-07-17T09:13:05.818461","created_date":"2025-10-10T00:00:00"}