{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T10:04:21Z","timestamp":1766484261883},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"18","license":[{"start":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T00:00:00Z","timestamp":1686873600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T00:00:00Z","timestamp":1686873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"published-print":{"date-parts":[[2023,12]]},"DOI":"10.1007\/s11227-023-05471-1","type":"journal-article","created":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T04:02:18Z","timestamp":1686888138000},"page":"20649-20664","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Efficient parallel kernel based on Cholesky decomposition to accelerate multichannel nonnegative matrix factorization"],"prefix":"10.1007","volume":"79","author":[{"given":"Antonio J.","family":"Mu\u00f1oz-Montoro","sequence":"first","affiliation":[]},{"given":"Julio J.","family":"Carabias-Orti","sequence":"additional","affiliation":[]},{"given":"Daniele","family":"Salvati","sequence":"additional","affiliation":[]},{"given":"Raquel","family":"Cortina","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,16]]},"reference":[{"issue":"1","key":"5471_CR1","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1109\/JETCAS.2019.2898948","volume":"9","author":"M Wien","year":"2019","unstructured":"Wien M, Boyce JM, Stockhammer T, Peng WH (2019) Standardization status of immersive video coding. IEEE J Emerg Select Top Circu Syst 9(1):5\u201317. https:\/\/doi.org\/10.1109\/JETCAS.2019.2898948","journal-title":"IEEE J Emerg Select Top Circu Syst"},{"key":"5471_CR2","doi-asserted-by":"publisher","unstructured":"Parry RM, Essa I (2006) Estimating the Spatial Position of Spectral Components in Audio. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). p. 666\u2013673. doi: https:\/\/doi.org\/10.1007\/11679363_83","DOI":"10.1007\/11679363_83"},{"key":"5471_CR3","doi-asserted-by":"publisher","unstructured":"FitzGerald D (2005) Non-negative tensor factorisation for sound source separation. In: IEE Irish Signals and Systems Conference 2005. vol. 2005. IEE. p. 8\u201312. doi: https:\/\/doi.org\/10.1049\/cp_20050279","DOI":"10.1049\/cp_20050279"},{"issue":"1","key":"5471_CR4","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1109\/LSP.2011.2173192","volume":"19","author":"S Lee","year":"2012","unstructured":"Lee S, Park SH, Sung KM (2012) Beamspace-domain multichannel nonnegative matrix factorization for audio source separation. IEEE Signal Process Lett 19(1):43\u201346. https:\/\/doi.org\/10.1109\/LSP.2011.2173192","journal-title":"IEEE Signal Process Lett"},{"key":"5471_CR5","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1109\/LSP.2021.3055463","volume":"28","author":"M Pezzoli","year":"2021","unstructured":"Pezzoli M, Carabias-Orti JJ, Cobos M, Antonacci F, Sarti A (2021) Ray-Space-based multichannel nonnegative matrix factorization for audio source separation. IEEE Signal Process Lett 28:369\u2013373. https:\/\/doi.org\/10.1109\/LSP.2021.3055463","journal-title":"IEEE Signal Process Lett"},{"key":"5471_CR6","doi-asserted-by":"crossref","unstructured":"Bianchi L, D\u2019Amelio F, Antonacci F, Sarti A, Tubaro S (2015) A plenacoustic approach to acoustic signal extraction. In: 2015 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA). p. 1\u20135","DOI":"10.1109\/WASPAA.2015.7336922"},{"issue":"12","key":"5471_CR7","doi-asserted-by":"publisher","first-page":"2481","DOI":"10.1109\/TASLP.2016.2615242","volume":"24","author":"D Markovi\u0107","year":"2016","unstructured":"Markovi\u0107 D, Antonacci F, Bianchi L, Tubaro S, Sarti A (2016) Extraction of acoustic sources through the processing of sound field maps in the ray space. IEEE\/ACM Trans Audio Speech Lang Process 24(12):2481\u20132494. https:\/\/doi.org\/10.1109\/TASLP.2016.2615242","journal-title":"IEEE\/ACM Trans Audio Speech Lang Process"},{"issue":"12","key":"5471_CR8","doi-asserted-by":"publisher","first-page":"2532","DOI":"10.1109\/TASL.2013.2277939","volume":"21","author":"Y Peled","year":"2013","unstructured":"Peled Y, Rafaely B (2013) Linearly-constrained minimum-variance method for spherical microphone arrays based on plane-wave decomposition of the sound field. IEEE Trans Audio Speech Langu Process 21(12):2532\u20132540. https:\/\/doi.org\/10.1109\/TASL.2013.2277939","journal-title":"IEEE Trans Audio Speech Langu Process"},{"key":"5471_CR9","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1109\/TASLP.2020.3045528","volume":"29","author":"Y Mitsufuji","year":"2021","unstructured":"Mitsufuji Y, Takamune N, Koyama S, Saruwatari H (2021) Multichannel blind source separation based on evanescent-region-aware non-negative tensor factorization in spherical harmonic domain. IEEE\/ACM Trans Audio Speech Langu Process 29:607\u2013617. https:\/\/doi.org\/10.1109\/TASLP.2020.3045528","journal-title":"IEEE\/ACM Trans Audio Speech Langu Process"},{"issue":"3","key":"5471_CR10","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1109\/TASLP.2014.2303576","volume":"22","author":"J Nikunen","year":"2014","unstructured":"Nikunen J, Virtanen T (2014) Direction of arrival based spatial covariance model for blind sound source separation. IEEE\/ACM Trans Audio Speech Langu Process 22(3):727\u2013739. https:\/\/doi.org\/10.1109\/TASLP.2014.2303576","journal-title":"IEEE\/ACM Trans Audio Speech Langu Process"},{"key":"5471_CR11","doi-asserted-by":"publisher","unstructured":"Ozerov A, F\u00e9votte C, Vincent E (2018) In: Makino S, editor. An Introduction to Multichannel NMF for Audio Source Separation. Cham: Springer International Publishing. p. 73\u201394. doi: https:\/\/doi.org\/10.1007\/978-3-319-73031-8_4","DOI":"10.1007\/978-3-319-73031-8_4"},{"issue":"9","key":"5471_CR12","doi-asserted-by":"publisher","first-page":"1512","DOI":"10.1109\/TASLP.2018.2830105","volume":"26","author":"JJ Carabias-Orti","year":"2018","unstructured":"Carabias-Orti JJ, Nikunen J, Virtanen T, Vera-Candeas P (2018) Multichannel blind sound source separation using spatial covariance model with level and time differences and nonnegative matrix factorization. IEEE\/ACM Trans Audio Speech Langu Process 26(9):1512\u20131527. https:\/\/doi.org\/10.1109\/TASLP.2018.2830105","journal-title":"IEEE\/ACM Trans Audio Speech Langu Process"},{"key":"5471_CR13","doi-asserted-by":"crossref","unstructured":"Sekiguchi K, Nugraha AA, Bando Y, Yoshii K (2019) Fast Multichannel Source Separation Based on Jointly Diagonalizable Spatial Covariance Matrices. In: 2019 27th European Signal Processing Conference (EUSIPCO). IEEE. p. 1\u20135. Available from: https:\/\/ieeexplore.ieee.org\/document\/8902557\/","DOI":"10.23919\/EUSIPCO.2019.8902557"},{"key":"5471_CR14","doi-asserted-by":"publisher","first-page":"17781","DOI":"10.1109\/ACCESS.2022.3150248","volume":"10","author":"AJ Mu\u00f1oz-Montoro","year":"2022","unstructured":"Mu\u00f1oz-Montoro AJ, Carabias-Orti JJ, Caba\u00f1as-Molero P, Ca\u00f1adas-Quesada FJ, Ruiz-Reyes N (2022) Multichannel blind music source separation using directivity-aware mnmf with harmonicity constraints. IEEE Access 10:17781\u201317795. https:\/\/doi.org\/10.1109\/ACCESS.2022.3150248","journal-title":"IEEE Access"},{"key":"5471_CR15","doi-asserted-by":"crossref","unstructured":"Sekiguchi K, Bando Y, Nugraha AA, Fontaine M, Yoshii K (2021) Autoregressive Fast Multichannel Nonnegative Matrix Factorization For Joint Blind Source Separation And Dereverberation. In: ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). p. 511\u2013515","DOI":"10.1109\/ICASSP39728.2021.9414857"},{"issue":"1","key":"5471_CR16","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1109\/JSTSP.2019.2901127","volume":"13","author":"S Koyama","year":"2019","unstructured":"Koyama S, Daudet L (2019) Sparse Representation of a spatial sound field in a reverberant environment. IEEE J Select Top Signal Process 13(1):172\u2013184. https:\/\/doi.org\/10.1109\/JSTSP.2019.2901127","journal-title":"IEEE J Select Top Signal Process"},{"key":"5471_CR17","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1109\/TASLP.2020.3045528","volume":"29","author":"Y Mitsufuji","year":"2021","unstructured":"Mitsufuji Y, Takamune N, Koyama S, Saruwatari H (2021) Multichannel blind source separation based on evanescent-region-aware non-negative tensor factorization in spherical harmonic domain. IEEE ACM Trans Audio Speech Lang Process 29:607\u2013617. https:\/\/doi.org\/10.1109\/TASLP.2020.3045528","journal-title":"IEEE ACM Trans Audio Speech Lang Process"},{"key":"5471_CR18","doi-asserted-by":"crossref","unstructured":"Borra F, Krenn S, Gebru ID, Markovi\u0107 D (2019) 1ST-Order Microphone Array System for Large Area Sound Field Recording and Reconstruction: Discussion and Preliminary Results. In: 2019 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA). p. 378\u2013382","DOI":"10.1109\/WASPAA.2019.8937281"},{"key":"5471_CR19","doi-asserted-by":"publisher","DOI":"10.1017\/9781108583664","volume-title":"Introduction to applied linear algebra : vectors matrices and least squares","author":"SP Boyd","year":"2018","unstructured":"Boyd SP, Lieven V (2018) Introduction to applied linear algebra\u202f: vectors matrices and least squares. Cambridge University Press, Cambridge UK"},{"key":"5471_CR20","doi-asserted-by":"crossref","unstructured":"Ito N, Nakatani T (2019) FastMNMF: Joint Diagonalization Based Accelerated Algorithms for Multichannel Nonnegative Matrix Factorization. In: ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE. p. 371\u2013375. Available from: https:\/\/ieeexplore.ieee.org\/document\/8682291\/","DOI":"10.1109\/ICASSP.2019.8682291"},{"key":"5471_CR21","doi-asserted-by":"publisher","first-page":"2610","DOI":"10.1109\/TASLP.2020.3019181","volume":"28","author":"K Sekiguchi","year":"2020","unstructured":"Sekiguchi K, Bando Y, Nugraha AA, Yoshii K, Kawahara T (2020) Fast multichannel nonnegative matrix factorization with directivity-aware jointly-diagonalizable spatial covariance matrices for blind source separation. IEEE\/ACM Trans Audio Speech Langu Process 28:2610\u20132625. https:\/\/doi.org\/10.1109\/TASLP.2020.3019181","journal-title":"IEEE\/ACM Trans Audio Speech Langu Process"},{"key":"5471_CR22","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1109\/TASLP.2019.2948770","volume":"28","author":"Y Mitsufuji","year":"2020","unstructured":"Mitsufuji Y, Uhlich S, Takamune N, Kitamura D, Koyama S, Saruwatari H (2020) Multichannel non-negative matrix factorization using banded spatial covariance matrices in wavenumber domain. IEEE\/ACM Trans Audio Speech Langu Process 28:49\u201360. https:\/\/doi.org\/10.1109\/TASLP.2019.2948770","journal-title":"IEEE\/ACM Trans Audio Speech Langu Process"},{"issue":"5","key":"5471_CR23","doi-asserted-by":"publisher","first-page":"971","DOI":"10.1109\/TASL.2013.2239990","volume":"21","author":"H Sawada","year":"2013","unstructured":"Sawada H, Kameoka H, Araki S, Ueda N (2013) Multichannel extensions of non-negative matrix factorization with complex-valued data. IEEE Trans Audio Speech Langu Process 21(5):971\u2013982. https:\/\/doi.org\/10.1109\/TASL.2013.2239990","journal-title":"IEEE Trans Audio Speech Langu Process"},{"issue":"12","key":"5471_CR24","doi-asserted-by":"publisher","first-page":"2354","DOI":"10.1109\/TASLP.2016.2608948","volume":"24","author":"SM N\u00f8rholm","year":"2016","unstructured":"N\u00f8rholm SM, Jensen JR, Christensen MG (2016) Instantaneous fundamental frequency estimation with optimal segmentation for nonstationary voiced speech. IEEE\/ACM Trans Audio Speech Langu Process 24(12):2354\u20132367. https:\/\/doi.org\/10.1109\/TASLP.2016.2608948","journal-title":"IEEE\/ACM Trans Audio Speech Langu Process"},{"issue":"9","key":"5471_CR25","doi-asserted-by":"publisher","first-page":"1599","DOI":"10.1109\/TASLP.2016.2573591","volume":"24","author":"A Kuklasi\u0144ski","year":"2016","unstructured":"Kuklasi\u0144ski A, Doclo S, Jensen SH, Jensen J (2016) Maximum likelihood PSD estimation for speech enhancement in reverberation and noise. IEEE\/ACM Trans Audio Speech Langu Process 24(9):1599\u20131612. https:\/\/doi.org\/10.1109\/TASLP.2016.2573591","journal-title":"IEEE\/ACM Trans Audio Speech Langu Process"},{"issue":"7","key":"5471_CR26","doi-asserted-by":"publisher","first-page":"3155","DOI":"10.1109\/TSP.2011.2119315","volume":"59","author":"A Liutkus","year":"2011","unstructured":"Liutkus A, Badeau R, Richard G (2011) Gaussian processes for underdetermined source separation. IEEE Trans Signal Process 59(7):3155\u20133167. https:\/\/doi.org\/10.1109\/TSP.2011.2119315","journal-title":"IEEE Trans Signal Process"},{"key":"5471_CR27","unstructured":"Yoshii K, Tomioka R, Mochihashi D, Goto M (2013) Beyond NMF: Time-Domain Audio Source Separation without Phase Reconstruction. In: ISMIR p. 369\u2013374"},{"issue":"6","key":"5471_CR28","doi-asserted-by":"publisher","first-page":"3261","DOI":"10.1137\/110821172","volume":"33","author":"J Kim","year":"2011","unstructured":"Kim J, Park H (2011) Fast nonnegative matrix factorization: an active-set-like method and comparisons. SIAM J Scient Comput 33(6):3261\u20133281. https:\/\/doi.org\/10.1137\/110821172","journal-title":"SIAM J Scient Comput"},{"key":"5471_CR29","doi-asserted-by":"publisher","unstructured":"Alostad JM (2017) Reducing Dimensionality Using NMF Based Cholesky Decomposition. In: Proceedings of the International Conference on Research in Adaptive and Convergent Systems. RACS \u201917. New York, NY, USA: Association for Computing Machinery. p. 49\u201355. doi: https:\/\/doi.org\/10.1145\/3129676.3129697","DOI":"10.1145\/3129676.3129697"},{"key":"5471_CR30","doi-asserted-by":"crossref","unstructured":"Nikunen J, Politis A (2018) Multichannel NMF for Source Separation with Ambisonic Signals. In: 2018 16th International Workshop on Acoustic Signal Enhancement (IWAENC). IEEE. p. 251\u2013255. Available from: https:\/\/ieeexplore.ieee.org\/document\/8521344\/","DOI":"10.1109\/IWAENC.2018.8521344"},{"issue":"3","key":"5471_CR31","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1109\/TASL.2010.2051355","volume":"19","author":"H Sawada","year":"2011","unstructured":"Sawada H, Araki S, Makino S (2011) Underdetermined convolutive blind source separation via frequency bin-wise clustering and permutation alignment. IEEE Trans Audio Speech Langu Process 19(3):516\u2013527. https:\/\/doi.org\/10.1109\/TASL.2010.2051355","journal-title":"IEEE Trans Audio Speech Langu Process"},{"issue":"3","key":"5471_CR32","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1177\/1094342018792079","volume":"33","author":"JV Ferreira Lima","year":"2019","unstructured":"Ferreira Lima JV, Ra\u00efs I, Lefevre L, Gautier T (2019) Performance and energy analysis of OpenMP runtime systems with dense linear algebra algorithms. The Int J High Perform Comput Appl 33(3):431\u2013443","journal-title":"The Int J High Perform Comput Appl"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-023-05471-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-023-05471-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-023-05471-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T21:04:21Z","timestamp":1697835861000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-023-05471-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,16]]},"references-count":32,"journal-issue":{"issue":"18","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["5471"],"URL":"https:\/\/doi.org\/10.1007\/s11227-023-05471-1","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"value":"0920-8542","type":"print"},{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,16]]},"assertion":[{"value":"8 March 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 June 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflicts of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}]}}