{"id":"https://openalex.org/W2209666225","doi":"https://doi.org/10.1109/spa.2015.7365111","title":"MRI image reconstruction approach for partial K-space based on the Discrete Fourier Transform in the least square sense","display_name":"MRI image reconstruction approach for partial K-space based on the Discrete Fourier Transform in the least square sense","publication_year":2015,"publication_date":"2015-09-01","ids":{"openalex":"https://openalex.org/W2209666225","doi":"https://doi.org/10.1109/spa.2015.7365111","mag":"2209666225"},"language":"en","primary_location":{"id":"doi:10.1109/spa.2015.7365111","is_oa":false,"landing_page_url":"https://doi.org/10.1109/spa.2015.7365111","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5004991371","display_name":"Kalim Tobaji","orcid":null},"institutions":[{"id":"https://openalex.org/I168913471","display_name":"University of Balamand","ror":"https://ror.org/01xvwxv41","country_code":"LB","type":"education","lineage":["https://openalex.org/I168913471"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"Kalim Tobaji","raw_affiliation_strings":["Department of Electrical Engineering, University of Balamand, Tripoli, Lebanon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Balamand, Tripoli, Lebanon","institution_ids":["https://openalex.org/I168913471"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054625877","display_name":"Laura Matar","orcid":null},"institutions":[{"id":"https://openalex.org/I168913471","display_name":"University of Balamand","ror":"https://ror.org/01xvwxv41","country_code":"LB","type":"education","lineage":["https://openalex.org/I168913471"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"Laura Matar","raw_affiliation_strings":["Department of Electrical Engineering, University of Balamand, Tripoli, Lebanon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Balamand, Tripoli, Lebanon","institution_ids":["https://openalex.org/I168913471"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039912757","display_name":"Antoine Abche","orcid":null},"institutions":[{"id":"https://openalex.org/I168913471","display_name":"University of Balamand","ror":"https://ror.org/01xvwxv41","country_code":"LB","type":"education","lineage":["https://openalex.org/I168913471"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"Antoine Abche","raw_affiliation_strings":["Department of Electrical Engineering, University of Balamand, Tripoli, Lebanon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Balamand, Tripoli, Lebanon","institution_ids":["https://openalex.org/I168913471"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073750953","display_name":"Elie G. Karam","orcid":"https://orcid.org/0000-0002-4681-8225"},"institutions":[{"id":"https://openalex.org/I168913471","display_name":"University of Balamand","ror":"https://ror.org/01xvwxv41","country_code":"LB","type":"education","lineage":["https://openalex.org/I168913471"]}],"countries":["LB"],"is_corresponding":false,"raw_author_name":"Elie Karam","raw_affiliation_strings":["Department of Electrical Engineering, University of Balamand, Tripoli, Lebanon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Balamand, Tripoli, Lebanon","institution_ids":["https://openalex.org/I168913471"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I168913471"],"apc_list":null,"apc_paid":null,"fwci":0.6851,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.68779124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"4","issue":null,"first_page":"44","last_page":"49"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.995199978351593,"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"}},"topics":[{"id":"https://openalex.org/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.995199978351593,"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"}},{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9923999905586243,"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"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9889000058174133,"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/square","display_name":"Square (algebra)","score":0.6129148602485657},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6062746644020081},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.5746290683746338},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.5738407373428345},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.562680184841156},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.51754230260849},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.5099154710769653},{"id":"https://openalex.org/keywords/k-space","display_name":"k-space","score":0.501279354095459},{"id":"https://openalex.org/keywords/sense","display_name":"Sense (electronics)","score":0.4597930908203125},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45918601751327515},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3899915814399719},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.3856385350227356},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3726668357849121},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3541385531425476},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.28895771503448486},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2796832323074341},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16392716765403748},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07013466954231262}],"concepts":[{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.6129148602485657},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6062746644020081},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.5746290683746338},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.5738407373428345},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.562680184841156},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.51754230260849},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.5099154710769653},{"id":"https://openalex.org/C197413143","wikidata":"https://www.wikidata.org/wiki/Q1050490","display_name":"k-space","level":3,"score":0.501279354095459},{"id":"https://openalex.org/C143141573","wikidata":"https://www.wikidata.org/wiki/Q7450971","display_name":"Sense (electronics)","level":2,"score":0.4597930908203125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45918601751327515},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3899915814399719},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.3856385350227356},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3726668357849121},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3541385531425476},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.28895771503448486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2796832323074341},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16392716765403748},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07013466954231262},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/spa.2015.7365111","is_oa":false,"landing_page_url":"https://doi.org/10.1109/spa.2015.7365111","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 Signal Processing: Algorithms, Architectures, Arrangements, and Applications (SPA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6000000238418579}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W320808933","https://openalex.org/W1561144482","https://openalex.org/W1712651094","https://openalex.org/W1971834088","https://openalex.org/W1991293234","https://openalex.org/W2021355263","https://openalex.org/W2056215075","https://openalex.org/W2060502676","https://openalex.org/W2087332491","https://openalex.org/W2101130594","https://openalex.org/W2106263593","https://openalex.org/W2129397292","https://openalex.org/W2144706786","https://openalex.org/W2165142794","https://openalex.org/W2792298817","https://openalex.org/W3023411394","https://openalex.org/W4285719527","https://openalex.org/W6633622198","https://openalex.org/W6664426724"],"related_works":["https://openalex.org/W4353087863","https://openalex.org/W2031403761","https://openalex.org/W3166675296","https://openalex.org/W2154898175","https://openalex.org/W2087332491","https://openalex.org/W3191591176","https://openalex.org/W4295678671","https://openalex.org/W2078960130","https://openalex.org/W1996797998","https://openalex.org/W3106540953"],"abstract_inverted_index":{"Magnetic":[0],"Resonance":[1],"Imaging":[2],"(MRI)":[3],"provides":[4],"important":[5],"and":[6,14,97,103,133],"valuable":[7],"information":[8],"(images)":[9],"about":[10],"the":[11,27,39,65,89,100,104,123,129,134,142,146],"organs":[12],"structures":[13],"soft":[15],"tissues":[16],"non-invasively.":[17],"In":[18],"this":[19],"work,":[20],"a":[21],"reconstruction":[22,119,150],"approach":[23,37],"using":[24,60,99],"partial":[25],"k-space,":[26],"\u201cOptimized":[28],"Discrete":[29],"Fourier":[30,41],"Transform\u201d":[31],"(ODFT),":[32],"is":[33,70,86,94,114],"introduced.":[34],"The":[35,50,92,138],"developed":[36],"decomposes":[38],"2-D":[40],"Transform":[42],"(FT)":[43],"into":[44],"two":[45],"steps":[46],"of":[47],"1-D":[48],"DFT.":[49],"corresponding":[51],"elements":[52],"along":[53],"each":[54],"row":[55],"or":[56],"column":[57],"are":[58],"estimated":[59],"an":[61,82],"optimization":[62],"technique,":[63,128],"namely,":[64],"complex":[66],"conjugate":[67],"gradient.":[68],"It":[69],"proposed":[71,143],"to":[72,80,88],"be":[73],"implemented":[74],"in":[75],"conjunction":[76],"with":[77,116],"other":[78],"techniques":[79,120],"obtain":[81],"optimum":[83],"image":[84,149],"that":[85,141],"closer":[87],"original":[90],"image.":[91],"algorithm":[93],"evaluated":[95],"visually":[96],"quantitatively":[98],"Performance":[101],"Test":[102],"Mean":[105],"Square":[106],"Error":[107],"as":[108,122],"similarity":[109],"measures.":[110],"Also,":[111],"its":[112],"effectiveness":[113],"compared":[115],"different":[117],"MRI":[118,148],"such":[121],"Projection":[124],"onto":[125],"Convex":[126],"Set":[127],"Conjugate":[130],"Synthesis":[131],"technique":[132,144],"Zero":[135],"filling":[136],"technique.":[137],"results":[139],"illustrate":[140],"outperforms":[145],"conventional":[147],"techniques.":[151]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
