Matrix Completion With Noise

On the heels of compressed sensing, a new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. In its simplest form, the pr...

Full description

Saved in:

Bibliographic Details
Published in	Proceedings of the IEEE Vol. 98; no. 6; pp. 925 - 936
Main Authors	Candes, Emmanuel J., Plan, Yaniv
Format	Journal Article
Language	English
Published	New York IEEE 01.06.2010 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects	Collaboration Compressed Compressed sensing Computer vision Detection duality in optimization Filtering Frequency Linear matrix inequalities low-rank matrices Machine learning Matrices matrix completion Minimization Motion pictures Noise Noise level nuclear-norm minimization Optimization oracle inequalities Quantitative analysis Remote sensing semidefinite programming Studies
Online Access	Get full text
ISSN	0018-9219 1558-2256 1558-2256
DOI	10.1109/JPROC.2009.2035722

Cover

Abstract	On the heels of compressed sensing, a new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. In its simplest form, the problem is to recover a matrix from a small sample of its entries. It comes up in many areas of science and engineering, including collaborative filtering, machine learning, control, remote sensing, and computer vision, to name a few. This paper surveys the novel literature on matrix completion, which shows that under some suitable conditions, one can recover an unknown low-rank matrix from a nearly minimal set of entries by solving a simple convex optimization problem, namely, nuclear-norm minimization subject to data constraints. Further, this paper introduces novel results showing that matrix completion is provably accurate even when the few observed entries are corrupted with a small amount of noise. A typical result is that one can recover an unknown matrix of low rank from just about log noisy samples with an error that is proportional to the noise level. We present numerical results that complement our quantitative analysis and show that, in practice, nuclear-norm minimization accurately fills in the many missing entries of large low-rank matrices from just a few noisy samples. Some analogies between matrix completion and compressed sensing are discussed throughout.
AbstractList	On the heels of compressed sensing, a new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. In its simplest form, the problem is to recover a matrix from a small sample of its entries. It comes up in many areas of science and engineering, including collaborative filtering, machine learning, control, remote sensing, and computer vision, to name a few. This paper surveys the novel literature on matrix completion, which shows that under some suitable conditions, one can recover an unknown low-rank matrix from a nearly minimal set of entries by solving a simple convex optimization problem, namely, nuclear-norm minimization subject to data constraints. Further, this paper introduces novel results showing that matrix completion is provably accurate even when the few observed entries are corrupted with a small amount of noise. A typical result is that one can recover an unknown [Formula Omitted] matrix of low rank [Formula Omitted] from just about [Formula Omitted] log [Formula Omitted] noisy samples with an error that is proportional to the noise level. We present numerical results that complement our quantitative analysis and show that, in practice, nuclear-norm minimization accurately fills in the many missing entries of large low-rank matrices from just a few noisy samples. Some analogies between matrix completion and compressed sensing are discussed throughout. On the heels of compressed sensing, a new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. In its simplest form, the problem is to recover a matrix from a small sample of its entries. It comes up in many areas of science and engineering, including collaborative filtering, machine learning, control, remote sensing, and computer vision, to name a few. This paper surveys the novel literature on matrix completion, which shows that under some suitable conditions, one can recover an unknown low-rank matrix from a nearly minimal set of entries by solving a simple convex optimization problem, namely, nuclear-norm minimization subject to data constraints. Further, this paper introduces novel results showing that matrix completion is provably accurate even when the few observed entries are corrupted with a small amount of noise. A typical result is that one can recover an unknown matrix of low rank from just about log noisy samples with an error that is proportional to the noise level. We present numerical results that complement our quantitative analysis and show that, in practice, nuclear-norm minimization accurately fills in the many missing entries of large low-rank matrices from just a few noisy samples. Some analogies between matrix completion and compressed sensing are discussed throughout. On the heels of compressed sensing, a new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be incomplete, and perhaps even corrupted, information. In its simplest form, the problem is to recover a matrix from a small sample of its entries. It comes up in many areas of science and engineering, including collaborative filtering, machine learning, control, remote sensing, and computer vision, to name a few. This paper surveys the novel literature on matrix completion, which shows that under some suitable conditions, one can recover an unknown low-rank matrix from a nearly minimal set of entries by solving a simple convex optimization problem, namely, nuclear-norm minimization subject to data constraints. Further, this paper introduces novel results showing that matrix completion is provably accurate even when the few observed entries are corrupted with a small amount of noise. A typical result is that one can recover an unknown n n matrix of low rank r from just about nr log 2 n noisy samples with an error that is proportional to the noise level. We present numerical results that complement our quantitative analysis and show that, in practice, nuclear-norm minimization accurately fills in the many missing entries of large low-rank matrices from just a few noisy samples. Some analogies between matrix completion and compressed sensing are discussed throughout.
Author	Candes, Emmanuel J. Plan, Yaniv
Author_xml	– sequence: 1 givenname: Emmanuel J. surname: Candes fullname: Candes, Emmanuel J. organization: Department of Applied and Computational Mathematics, California Institute of Technology, Pasadena, CA, USA – sequence: 2 givenname: Yaniv surname: Plan fullname: Plan, Yaniv organization: Department of Applied and Computational Mathematics, California Institute of Technology, Pasadena, CA, USA
BookMark	eNptkD1PwzAQhi1UJNrCHwCGSiwsKT47tuMRVXyqUIRAjJadOMJVmoQ4EfTfk5CqQ8RyHu59zvfcBI3yIrcInQKeA2B59fjyulrMCcayLZQJQg7QGBiLAkIYH6ExxhAFkoA8QhPv1xi3KU7H6PxJ15X7mS2KTZnZ2hX57MPVn7Pnwnl7jA5TnXl7snun6P325m1xHyxXdw-L62UQU0HqwBopQTCqrUi00VGcpizhMREUkhBLMFJwg42RkeGcJhFjhAsDKY5MDCloOkW0n9vkpd5-6yxTZeU2utoqwKoTVOuyKmLVCaqdYEtd9lTb-mqsr9XG-dhmmc5t0XgFXAChICLRRi8G0XXRVHnr1H5ABEgc4m5g1KfiqvC-sqmKXa27m9SVdtl-l79jD3chA3Qo8C901kPOWrsHWMjCEHP6C5W5iNo
CODEN	IEEPAD
CitedBy_id	crossref_primary_10_1007_s10115_013_0713_z crossref_primary_10_1016_j_laa_2021_06_011 crossref_primary_10_1587_transcom_2019EBP3230 crossref_primary_10_1109_TIT_2011_2143970 crossref_primary_10_1371_journal_pcbi_1005506 crossref_primary_10_1080_01621459_2021_1891924 crossref_primary_10_1109_JSAC_2019_2904347 crossref_primary_10_1109_TIT_2013_2240435 crossref_primary_10_1109_TVT_2021_3105673 crossref_primary_10_1002_cmmi_1543 crossref_primary_10_1049_rsn2_12074 crossref_primary_10_1007_s11075_023_01662_2 crossref_primary_10_1214_18_AOS1742 crossref_primary_10_1016_j_sigpro_2022_108580 crossref_primary_10_1016_j_vlsi_2016_08_006 crossref_primary_10_1109_TGRS_2013_2284280 crossref_primary_10_1109_TIP_2018_2865837 crossref_primary_10_1016_j_neucom_2018_05_092 crossref_primary_10_1109_TMC_2017_2775230 crossref_primary_10_1109_TNNLS_2023_3280086 crossref_primary_10_7717_peerj_cs_231 crossref_primary_10_1109_TIT_2022_3196707 crossref_primary_10_3390_a16010012 crossref_primary_10_1109_TSG_2019_2956906 crossref_primary_10_1109_TIT_2023_3273181 crossref_primary_10_1109_TSP_2020_3032234 crossref_primary_10_1109_TSP_2021_3139213 crossref_primary_10_1111_ele_14059 crossref_primary_10_3102_1076998616676407 crossref_primary_10_1137_15M104726X crossref_primary_10_1109_JSTSP_2012_2195472 crossref_primary_10_3934_bdia_2016001 crossref_primary_10_1016_j_jvcir_2015_06_012 crossref_primary_10_1109_TIT_2024_3350518 crossref_primary_10_1109_TSG_2018_2848935 crossref_primary_10_1109_LSP_2024_3379830 crossref_primary_10_1109_TSP_2013_2295557 crossref_primary_10_1214_21_AOS2061 crossref_primary_10_3390_rs14164120 crossref_primary_10_1093_bib_bbab479 crossref_primary_10_1109_TSP_2013_2279080 crossref_primary_10_1007_s11276_018_1663_x crossref_primary_10_1214_21_AOS2066 crossref_primary_10_1109_TGRS_2019_2907801 crossref_primary_10_1109_TPAMI_2012_271 crossref_primary_10_1146_annurev_control_091819_074326 crossref_primary_10_1109_JSEN_2019_2906375 crossref_primary_10_1007_s40314_018_0613_7 crossref_primary_10_1214_21_EJS1935 crossref_primary_10_1002_anie_201409291 crossref_primary_10_1016_j_cam_2023_115557 crossref_primary_10_1016_j_neucom_2017_09_052 crossref_primary_10_1109_TKDE_2019_2962031 crossref_primary_10_3934_ipi_2017030 crossref_primary_10_1016_j_trip_2022_100555 crossref_primary_10_1109_TVT_2024_3495536 crossref_primary_10_1109_TCYB_2018_2837675 crossref_primary_10_3390_rs14153790 crossref_primary_10_1016_j_media_2017_02_008 crossref_primary_10_1109_TAC_2021_3137147 crossref_primary_10_1587_transcom_2018EBP3289 crossref_primary_10_2139_ssrn_4372280 crossref_primary_10_1109_TSP_2015_2449254 crossref_primary_10_3150_23_BEJ1675 crossref_primary_10_1109_LSP_2017_2685518 crossref_primary_10_1364_OE_24_020069 crossref_primary_10_1016_j_ins_2022_08_087 crossref_primary_10_1109_TPDS_2023_3274305 crossref_primary_10_1109_TIT_2023_3331010 crossref_primary_10_1109_TGRS_2020_2996686 crossref_primary_10_1371_journal_pone_0098441 crossref_primary_10_1016_j_neucom_2015_05_146 crossref_primary_10_1109_TSP_2014_2357773 crossref_primary_10_1016_j_sysconle_2013_04_005 crossref_primary_10_1002_cjs_70002 crossref_primary_10_1038_lsa_2017_179 crossref_primary_10_1049_iet_ipr_2019_1648 crossref_primary_10_1109_TCYB_2023_3305552 crossref_primary_10_1190_geo2015_0341_1 crossref_primary_10_1016_j_sigpro_2019_07_028 crossref_primary_10_1111_1365_2478_12949 crossref_primary_10_1016_j_jeconom_2024_105684 crossref_primary_10_1016_j_procs_2013_05_021 crossref_primary_10_1142_S0217595913400101 crossref_primary_10_1049_iet_ipr_2019_1654 crossref_primary_10_1109_TGRS_2021_3053201 crossref_primary_10_1007_s10957_019_01477_z crossref_primary_10_1007_s10915_024_02636_9 crossref_primary_10_1016_j_jeconom_2024_105682 crossref_primary_10_1088_1361_6420_ab3204 crossref_primary_10_1007_s10994_023_06338_5 crossref_primary_10_1016_j_infrared_2024_105676 crossref_primary_10_1109_TIT_2022_3170244 crossref_primary_10_3390_s18072377 crossref_primary_10_1109_TCOMM_2014_2346775 crossref_primary_10_1121_10_0002175 crossref_primary_10_1109_TGRS_2017_2709250 crossref_primary_10_1007_s10208_015_9256_x crossref_primary_10_1016_j_patrec_2016_12_019 crossref_primary_10_1137_21M141703X crossref_primary_10_1109_TRS_2024_3362693 crossref_primary_10_1016_j_patcog_2017_05_013 crossref_primary_10_1109_TPAMI_2019_2906603 crossref_primary_10_1109_LSP_2025_3539252 crossref_primary_10_1137_16M1062089 crossref_primary_10_1109_TIP_2014_2352497 crossref_primary_10_1109_TIT_2013_2257913 crossref_primary_10_1109_TSP_2023_3251110 crossref_primary_10_1093_bib_bbab328 crossref_primary_10_1214_20_AOAS1356 crossref_primary_10_1016_j_jvcir_2021_103335 crossref_primary_10_1109_TIT_2014_2311661 crossref_primary_10_1109_TIT_2017_2701342 crossref_primary_10_2140_tunis_2024_6_543 crossref_primary_10_3390_s22124625 crossref_primary_10_1109_TNET_2018_2888600 crossref_primary_10_1109_TIT_2023_3317168 crossref_primary_10_1016_j_ins_2023_119562 crossref_primary_10_1109_ACCESS_2024_3516506 crossref_primary_10_1109_TGRS_2015_2489218 crossref_primary_10_1109_TCI_2017_2693966 crossref_primary_10_1088_1361_6579_aba492 crossref_primary_10_1016_j_sigpro_2015_09_036 crossref_primary_10_1007_s10208_020_09471_y crossref_primary_10_1007_s11263_013_0684_2 crossref_primary_10_1155_2014_420856 crossref_primary_10_1016_j_knosys_2021_107053 crossref_primary_10_14778_3397230_3397235 crossref_primary_10_1016_j_acha_2023_03_007 crossref_primary_10_1021_jz3009369 crossref_primary_10_1109_TCNS_2022_3203798 crossref_primary_10_1109_TIT_2018_2809782 crossref_primary_10_1109_TKDE_2016_2569096 crossref_primary_10_3390_rs9101044 crossref_primary_10_1109_TIP_2017_2781425 crossref_primary_10_1098_rspa_2023_0121 crossref_primary_10_1016_j_trc_2017_09_011 crossref_primary_10_1109_TSP_2021_3051425 crossref_primary_10_1214_21_AOS2146 crossref_primary_10_1007_s10957_021_01956_2 crossref_primary_10_1007_s10994_017_5667_z crossref_primary_10_1088_1361_665X_ac50f4 crossref_primary_10_1109_TIT_2021_3111828 crossref_primary_10_1016_j_acha_2016_09_005 crossref_primary_10_1007_s41095_016_0056_2 crossref_primary_10_1016_j_energy_2020_117775 crossref_primary_10_1109_JPROC_2018_2844126 crossref_primary_10_1145_3264961 crossref_primary_10_2139_ssrn_4006034 crossref_primary_10_1109_LSP_2020_2988596 crossref_primary_10_1051_matecconf_201817601018 crossref_primary_10_1016_j_ijforecast_2018_03_008 crossref_primary_10_1016_j_sigpro_2022_108480 crossref_primary_10_1109_TSP_2011_2161982 crossref_primary_10_1109_TSP_2011_2161984 crossref_primary_10_1109_TPAMI_2016_2608882 crossref_primary_10_1016_j_ymssp_2025_112565 crossref_primary_10_1002_cpe_5701 crossref_primary_10_1109_ACCESS_2018_2880454 crossref_primary_10_1109_TIT_2017_2695601 crossref_primary_10_1016_j_jvcir_2017_11_019 crossref_primary_10_1109_TSP_2016_2569479 crossref_primary_10_1109_TAES_2015_140452 crossref_primary_10_1109_TSP_2017_2711501 crossref_primary_10_1109_JSTSP_2020_3038054 crossref_primary_10_1137_16M1078318 crossref_primary_10_1007_s11228_017_0421_z crossref_primary_10_1109_TIP_2020_3044472 crossref_primary_10_1109_LSP_2018_2872400 crossref_primary_10_1214_15_AOS1426 crossref_primary_10_1109_TIP_2015_2441632 crossref_primary_10_3390_math11122674 crossref_primary_10_1002_mrm_24997 crossref_primary_10_3390_s23187848 crossref_primary_10_1109_TIFS_2020_2975925 crossref_primary_10_1016_j_comnet_2017_09_001 crossref_primary_10_1109_TNNLS_2020_2980960 crossref_primary_10_1016_j_jsv_2016_02_031 crossref_primary_10_1109_TIT_2015_2466597 crossref_primary_10_3390_axioms7030051 crossref_primary_10_1214_15_EJS1020 crossref_primary_10_1007_BF03549586 crossref_primary_10_1093_bioinformatics_btx597 crossref_primary_10_1007_s11766_020_4136_3 crossref_primary_10_1109_ACCESS_2018_2887261 crossref_primary_10_1109_TIP_2015_2503238 crossref_primary_10_1109_MSP_2010_939733 crossref_primary_10_1109_TNNLS_2012_2188906 crossref_primary_10_1111_poms_13582 crossref_primary_10_1190_geo2019_0586_1 crossref_primary_10_1186_s13408_019_0077_0 crossref_primary_10_1093_bioinformatics_btab322 crossref_primary_10_1109_TNNLS_2023_3288769 crossref_primary_10_1109_TSP_2021_3085116 crossref_primary_10_1017_S0963548321000249 crossref_primary_10_3390_rs16111837 crossref_primary_10_1049_iet_spr_2018_5114 crossref_primary_10_1109_TSMCB_2011_2168953 crossref_primary_10_1109_TVT_2023_3290181 crossref_primary_10_1109_TGRS_2020_3002724 crossref_primary_10_1145_3404374 crossref_primary_10_1109_TGRS_2017_2771155 crossref_primary_10_1016_j_neunet_2017_08_001 crossref_primary_10_1016_j_orl_2019_08_001 crossref_primary_10_1080_0952813X_2015_1042532 crossref_primary_10_1214_15_EJS1093 crossref_primary_10_1016_j_patcog_2019_02_011 crossref_primary_10_1109_ACCESS_2021_3076797 crossref_primary_10_1109_TSP_2021_3113468 crossref_primary_10_1016_j_laa_2017_11_014 crossref_primary_10_3389_fmicb_2023_1179414 crossref_primary_10_1109_ACCESS_2020_2996303 crossref_primary_10_1109_TPDS_2019_2954902 crossref_primary_10_1109_TSP_2016_2613070 crossref_primary_10_1016_j_jfa_2022_109593 crossref_primary_10_1080_07350015_2021_1954527 crossref_primary_10_1007_s10472_020_09717_z crossref_primary_10_1109_TSG_2024_3471077 crossref_primary_10_1109_JSTSP_2021_3063837 crossref_primary_10_1109_TSP_2018_2867995 crossref_primary_10_1155_2014_353970 crossref_primary_10_1088_1742_6596_787_1_012008 crossref_primary_10_1109_ACCESS_2019_2894784 crossref_primary_10_1109_TNNLS_2022_3183970 crossref_primary_10_1109_JSEN_2019_2912642 crossref_primary_10_1109_TIP_2011_2177989 crossref_primary_10_1016_j_engappai_2023_106659 crossref_primary_10_1016_j_patrec_2016_05_029 crossref_primary_10_1137_141002165 crossref_primary_10_1109_TIT_2020_3039308 crossref_primary_10_1137_19M1290000 crossref_primary_10_1109_JSTSP_2012_2237381 crossref_primary_10_1109_TIT_2011_2111190 crossref_primary_10_1109_JPROC_2015_2474704 crossref_primary_10_1109_JSEN_2024_3393761 crossref_primary_10_1109_TKDE_2020_3005978 crossref_primary_10_1002_sta4_70003 crossref_primary_10_1007_s11042_017_5263_z crossref_primary_10_1007_s00362_018_1043_8 crossref_primary_10_4236_am_2017_82019 crossref_primary_10_1109_TIM_2022_3203097 crossref_primary_10_1016_j_acha_2016_08_004 crossref_primary_10_1109_TIT_2019_2950715 crossref_primary_10_1109_TIP_2012_2192742 crossref_primary_10_1109_ACCESS_2018_2877432 crossref_primary_10_1109_LGRS_2015_2461654 crossref_primary_10_1109_OJCSYS_2022_3200015 crossref_primary_10_1016_j_laa_2017_07_016 crossref_primary_10_3390_rs10071053 crossref_primary_10_1007_s11222_020_09963_5 crossref_primary_10_1109_TIT_2023_3284341 crossref_primary_10_1109_JSTSP_2016_2535182 crossref_primary_10_1007_s11045_017_0531_7 crossref_primary_10_1007_s10115_021_01628_7 crossref_primary_10_1016_j_physrep_2012_02_006 crossref_primary_10_1214_15_EJS1076 crossref_primary_10_7566_JPSJ_89_012001 crossref_primary_10_1016_j_cam_2017_03_014 crossref_primary_10_1109_LCSYS_2018_2845943 crossref_primary_10_1109_TSP_2017_2695450 crossref_primary_10_2200_S00640ED1V01Y201504IVM018 crossref_primary_10_1214_19_EJS1582 crossref_primary_10_1016_j_comnet_2012_02_017 crossref_primary_10_1080_10618600_2018_1482763 crossref_primary_10_1109_TIP_2011_2156801 crossref_primary_10_1109_TIP_2018_2874284 crossref_primary_10_1109_TNNLS_2022_3182541 crossref_primary_10_1109_JSTSP_2015_2469641 crossref_primary_10_1137_21M1416849 crossref_primary_10_1137_110853996 crossref_primary_10_1016_j_cam_2017_12_048 crossref_primary_10_1016_j_knosys_2017_02_031 crossref_primary_10_1109_TIP_2016_2540810 crossref_primary_10_2139_ssrn_4568525 crossref_primary_10_1093_biomet_asaa006 crossref_primary_10_1109_TIM_2022_3204072 crossref_primary_10_1049_iet_spr_2018_5102 crossref_primary_10_1137_20M1315294 crossref_primary_10_1080_10618600_2019_1585261 crossref_primary_10_1007_s11075_020_00876_y crossref_primary_10_1007_s11075_023_01513_0 crossref_primary_10_1109_TAES_2018_2847958 crossref_primary_10_1109_TNNLS_2018_2885699 crossref_primary_10_1007_s10107_016_1090_7 crossref_primary_10_1002_cpa_21432 crossref_primary_10_1109_OJCSYS_2023_3315088 crossref_primary_10_1137_15M1025153 crossref_primary_10_3389_fgene_2019_00009 crossref_primary_10_3934_ipi_2012_6_357 crossref_primary_10_1016_j_sigpro_2016_07_034 crossref_primary_10_1109_LSP_2022_3229555 crossref_primary_10_1109_JSTSP_2016_2539123 crossref_primary_10_1186_s13634_016_0360_0 crossref_primary_10_1016_j_ejor_2016_07_014 crossref_primary_10_3150_19_BEJ1114 crossref_primary_10_1016_j_neucom_2018_07_066 crossref_primary_10_3390_e25020333 crossref_primary_10_1109_TASE_2020_2997718 crossref_primary_10_1137_100817206 crossref_primary_10_1190_geo2013_0022_1 crossref_primary_10_1214_10_AOS860 crossref_primary_10_3390_s22155548 crossref_primary_10_1109_TIT_2022_3205781 crossref_primary_10_1109_ACCESS_2019_2894622 crossref_primary_10_1103_PhysRevA_86_012512 crossref_primary_10_1109_TGRS_2020_3027819 crossref_primary_10_1109_LGRS_2025_3527696 crossref_primary_10_1103_PhysRevA_87_030102 crossref_primary_10_1016_j_chemolab_2018_04_001 crossref_primary_10_1109_LCSYS_2021_3133798 crossref_primary_10_1109_TNET_2019_2953921 crossref_primary_10_1214_24_AOS2366 crossref_primary_10_1109_TSP_2011_2161471 crossref_primary_10_1002_mrm_26079 crossref_primary_10_1109_TSP_2018_2876305 crossref_primary_10_1109_TIT_2011_2136318 crossref_primary_10_1109_TIP_2016_2642784 crossref_primary_10_1016_j_orl_2022_01_007 crossref_primary_10_1109_TIT_2016_2598574 crossref_primary_10_1109_TIT_2021_3050469 crossref_primary_10_1137_120862843 crossref_primary_10_1016_j_neucom_2016_11_068 crossref_primary_10_1080_10618600_2018_1518238 crossref_primary_10_1109_TSC_2021_3065035 crossref_primary_10_1109_TBME_2013_2264772 crossref_primary_10_1016_j_sigpro_2016_07_018 crossref_primary_10_1109_TNNLS_2023_3327716 crossref_primary_10_1109_TSP_2022_3230332 crossref_primary_10_1016_j_sigpro_2024_109656 crossref_primary_10_1109_TGRS_2021_3100715 crossref_primary_10_1073_pnas_2302930120 crossref_primary_10_1109_MCOM_2016_7588229 crossref_primary_10_1007_s10994_017_5673_1 crossref_primary_10_1007_s11425_016_9107_y crossref_primary_10_1109_LCOMM_2018_2804396 crossref_primary_10_1007_s10107_015_0961_7 crossref_primary_10_1109_TIP_2017_2768185 crossref_primary_10_1109_TIT_2011_2104999 crossref_primary_10_3390_eng5010021 crossref_primary_10_1016_j_neucom_2017_11_021 crossref_primary_10_1109_TBC_2014_2345931 crossref_primary_10_1109_TKDE_2024_3419698 crossref_primary_10_1007_s10489_021_03137_0 crossref_primary_10_1016_j_knosys_2015_06_001 crossref_primary_10_1109_TSP_2019_2946022 crossref_primary_10_1109_JSTSP_2016_2539100 crossref_primary_10_1109_TSP_2014_2385040 crossref_primary_10_3390_e20030171 crossref_primary_10_1002_wics_1469 crossref_primary_10_1007_s10618_017_0516_z crossref_primary_10_1109_TSP_2019_2946026 crossref_primary_10_1137_17M1115770 crossref_primary_10_1080_03610918_2023_2242013 crossref_primary_10_1109_TKDE_2020_2983708 crossref_primary_10_3390_info10040124 crossref_primary_10_1007_s40687_023_00381_3 crossref_primary_10_1109_JSAC_2024_3414589 crossref_primary_10_1109_LSP_2020_3025478 crossref_primary_10_1016_j_patcog_2010_11_012 crossref_primary_10_1007_s10618_013_0341_y crossref_primary_10_1002_sta4_303 crossref_primary_10_1088_1612_202X_aa7b96 crossref_primary_10_1109_TIT_2014_2343623 crossref_primary_10_1049_ipr2_12040 crossref_primary_10_1145_3658148 crossref_primary_10_1016_j_procs_2015_05_422 crossref_primary_10_1109_TIT_2018_2816685 crossref_primary_10_1142_S0219691317500321 crossref_primary_10_1007_s40305_015_0080_4 crossref_primary_10_1007_s12532_012_0044_1 crossref_primary_10_1109_LSP_2020_2970306 crossref_primary_10_1016_j_laa_2016_04_017 crossref_primary_10_1145_3278607 crossref_primary_10_1088_1742_5468_aabc7d crossref_primary_10_1109_TIT_2017_2713822 crossref_primary_10_1007_s13042_017_0665_9 crossref_primary_10_1007_s10107_015_0876_3 crossref_primary_10_1002_cnm_3858 crossref_primary_10_1016_j_acha_2011_04_004 crossref_primary_10_1109_TAES_2017_2717518 crossref_primary_10_1016_j_laa_2020_01_036 crossref_primary_10_1002_nbm_4695 crossref_primary_10_1111_1365_2478_13123 crossref_primary_10_1007_s40687_023_00414_x crossref_primary_10_1016_j_neucom_2012_04_043 crossref_primary_10_1109_LGRS_2014_2300170 crossref_primary_10_1109_TMC_2016_2595569 crossref_primary_10_1109_TSP_2019_2916100 crossref_primary_10_1080_14498596_2018_1509740 crossref_primary_10_1080_00401706_2020_1801256 crossref_primary_10_1109_TCYB_2022_3224070 crossref_primary_10_1109_TVT_2020_2986783 crossref_primary_10_1007_s11222_021_10033_7 crossref_primary_10_1109_TGRS_2025_3527056 crossref_primary_10_1109_TNET_2014_2337371 crossref_primary_10_1109_TCYB_2014_2351831 crossref_primary_10_1016_j_jmsy_2022_03_001 crossref_primary_10_1016_j_dsp_2021_103242 crossref_primary_10_1109_TCOMM_2016_2623606 crossref_primary_10_1186_s13638_020_01724_2 crossref_primary_10_1109_TIP_2016_2547180 crossref_primary_10_1016_j_rse_2021_112649 crossref_primary_10_1186_s43593_022_00038_8 crossref_primary_10_1007_s10994_013_5366_3 crossref_primary_10_3150_12_BEJSP17 crossref_primary_10_3390_a10010029 crossref_primary_10_1515_jiip_2023_0009 crossref_primary_10_1587_transfun_E100_A_1279 crossref_primary_10_1080_01621459_2024_2380105 crossref_primary_10_1109_JSTSP_2018_2827299 crossref_primary_10_1109_TIT_2021_3138772 crossref_primary_10_1016_j_laa_2021_03_039 crossref_primary_10_1016_j_dsp_2021_103009 crossref_primary_10_1007_s11767_013_3049_7 crossref_primary_10_1016_j_jvcir_2014_01_015 crossref_primary_10_1109_JSYST_2020_3012775 crossref_primary_10_1142_S0218001415510039 crossref_primary_10_3389_fams_2018_00065 crossref_primary_10_1080_01621459_2019_1635485 crossref_primary_10_1007_s00521_016_2391_8 crossref_primary_10_1109_TIT_2011_2171521 crossref_primary_10_1007_s11263_016_0881_x crossref_primary_10_1016_j_crmeth_2023_100540 crossref_primary_10_1109_TSC_2021_3089241 crossref_primary_10_1016_j_cam_2022_114866 crossref_primary_10_1109_OJSP_2021_3104497 crossref_primary_10_1109_TSP_2013_2278516 crossref_primary_10_1214_19_EJS1630 crossref_primary_10_1109_TFUZZ_2017_2760287 crossref_primary_10_1109_TCYB_2018_2811764 crossref_primary_10_1093_imaiai_iaaa020 crossref_primary_10_1017_jfm_2016_682 crossref_primary_10_1214_17_AOS1541 crossref_primary_10_1007_s11424_023_2342_2 crossref_primary_10_1109_TSP_2016_2645517 crossref_primary_10_1109_TSP_2018_2883924 crossref_primary_10_1007_s10994_024_06691_z crossref_primary_10_1214_17_AOS1666 crossref_primary_10_3390_e24070946 crossref_primary_10_1103_PhysRevLett_105_150401 crossref_primary_10_3390_sym11101277 crossref_primary_10_1109_TPAMI_2012_88 crossref_primary_10_1186_s13634_018_0591_3 crossref_primary_10_1109_TIT_2019_2924900 crossref_primary_10_3390_s24082485 crossref_primary_10_1016_j_jcss_2022_12_001 crossref_primary_10_1109_TSP_2021_3067738 crossref_primary_10_1145_2674559 crossref_primary_10_1109_TIP_2015_2511584 crossref_primary_10_1109_MSP_2012_2232355 crossref_primary_10_1137_130919490 crossref_primary_10_1109_TCBB_2021_3109055 crossref_primary_10_1109_LSP_2012_2224655 crossref_primary_10_3182_20120711_3_BE_2027_00244 crossref_primary_10_1007_s10589_021_00279_2 crossref_primary_10_1007_s43670_024_00096_8 crossref_primary_10_1007_s00521_017_3216_0 crossref_primary_10_1109_TGRS_2018_2872590 crossref_primary_10_3390_app9081669 crossref_primary_10_1109_TSP_2014_2325798 crossref_primary_10_1007_s11263_014_0746_0 crossref_primary_10_1007_s13042_023_01935_1 crossref_primary_10_1109_TIT_2022_3144605 crossref_primary_10_1109_TKDE_2014_2356461 crossref_primary_10_1016_j_neucom_2021_07_075 crossref_primary_10_1007_s13177_018_0175_5 crossref_primary_10_1007_s10483_014_1860_9 crossref_primary_10_1109_LSP_2020_3008043 crossref_primary_10_1137_130932168 crossref_primary_10_1137_130935434 crossref_primary_10_1214_22_AOS2223 crossref_primary_10_1016_j_neucom_2015_02_082 crossref_primary_10_1002_cpa_21957 crossref_primary_10_1016_j_sigpro_2022_108826 crossref_primary_10_1109_TIP_2019_2957925 crossref_primary_10_3390_sym11111377 crossref_primary_10_1214_20_AOS1942 crossref_primary_10_1145_3700433 crossref_primary_10_1093_imaiai_iay003 crossref_primary_10_1109_TSP_2012_2197748 crossref_primary_10_1118_1_4921365 crossref_primary_10_1007_s10915_021_01654_1 crossref_primary_10_1002_mrm_25395 crossref_primary_10_1109_JIOT_2019_2950418 crossref_primary_10_1016_j_imavis_2014_02_007 crossref_primary_10_1002_nbm_5223 crossref_primary_10_1109_TIT_2016_2556702 crossref_primary_10_1137_18M1202311 crossref_primary_10_1016_j_sigpro_2016_05_026 crossref_primary_10_1137_21M1402340 crossref_primary_10_1007_s13042_014_0241_5 crossref_primary_10_1080_01621459_2024_2335591 crossref_primary_10_1109_TPAMI_2019_2929043 crossref_primary_10_1287_trsc_2023_0493 crossref_primary_10_1111_rssb_12400 crossref_primary_10_2139_ssrn_4747889 crossref_primary_10_1109_ACCESS_2019_2961787 crossref_primary_10_1109_TIP_2021_3086596 crossref_primary_10_1109_TIT_2016_2549040 crossref_primary_10_3390_rs17060982 crossref_primary_10_1109_TGRS_2023_3247689 crossref_primary_10_1016_j_cageo_2019_104376 crossref_primary_10_1109_TIT_2013_2294644 crossref_primary_10_1021_acs_jctc_3c00851 crossref_primary_10_1117_1_JRS_10_035014 crossref_primary_10_1109_TNET_2012_2228881 crossref_primary_10_1109_TSP_2022_3173470 crossref_primary_10_1137_130921179 crossref_primary_10_1016_j_acha_2024_101746 crossref_primary_10_1109_TCYB_2021_3113520 crossref_primary_10_1109_TGRS_2023_3237464 crossref_primary_10_1109_TIP_2014_2380155 crossref_primary_10_1109_TAC_2022_3161876 crossref_primary_10_1162_NECO_a_00369 crossref_primary_10_1016_j_acha_2021_03_004 crossref_primary_10_1093_ije_dyac043 crossref_primary_10_1093_imaiai_iay019 crossref_primary_10_1109_TIM_2021_3109743 crossref_primary_10_1038_srep17728 crossref_primary_10_1109_TBDATA_2017_2763170 crossref_primary_10_1007_s11704_016_5552_0 crossref_primary_10_5802_ojmo_27 crossref_primary_10_1109_JSEN_2016_2558184 crossref_primary_10_1109_TSP_2022_3229642 crossref_primary_10_1049_ipr2_12551 crossref_primary_10_1088_1361_6420_ab6139 crossref_primary_10_3390_info8010017 crossref_primary_10_1109_TSP_2015_2417491 crossref_primary_10_1016_j_sigpro_2021_107993 crossref_primary_10_1109_TSP_2018_2818075 crossref_primary_10_1214_19_AOS1819 crossref_primary_10_1137_20M1319577 crossref_primary_10_1111_jcmm_14048 crossref_primary_10_1109_TGRS_2016_2623626 crossref_primary_10_1109_JSTARS_2022_3162763 crossref_primary_10_1109_LGRS_2018_2810234 crossref_primary_10_1021_pr500171u crossref_primary_10_1109_TIP_2019_2917857 crossref_primary_10_3390_math8040628 crossref_primary_10_1109_TGRS_2023_3282217 crossref_primary_10_1109_TSP_2022_3174423 crossref_primary_10_1007_s11063_017_9715_2 crossref_primary_10_1109_TCSVT_2023_3250651 crossref_primary_10_1109_TPAMI_2016_2539946 crossref_primary_10_1109_TSP_2019_2904026 crossref_primary_10_1007_s11265_022_01817_9 crossref_primary_10_3390_s17030542 crossref_primary_10_1039_C7JA00178A crossref_primary_10_1214_14_AOS1272 crossref_primary_10_3934_fods_2021028 crossref_primary_10_1109_TCYB_2017_2715846 crossref_primary_10_1109_TNNLS_2016_2597444 crossref_primary_10_1038_s44172_025_00345_1 crossref_primary_10_1109_JSTSP_2012_2233193 crossref_primary_10_3390_a9020028 crossref_primary_10_1016_j_comcom_2018_03_007 crossref_primary_10_1109_TSP_2016_2597121 crossref_primary_10_1016_j_asoc_2024_112075 crossref_primary_10_1093_ectj_utae014 crossref_primary_10_1109_TCYB_2013_2286106 crossref_primary_10_1093_imaiai_iax020 crossref_primary_10_1109_JSTSP_2021_3079626 crossref_primary_10_12677_PM_2021_116114 crossref_primary_10_1109_TIT_2023_3237231 crossref_primary_10_1109_TKDE_2012_75 crossref_primary_10_1121_10_0017064 crossref_primary_10_1214_19_EJS1658 crossref_primary_10_1109_TGRS_2017_2771826 crossref_primary_10_1109_TKDE_2020_2995896 crossref_primary_10_1007_s11517_020_02312_8 crossref_primary_10_1049_rsn2_12110 crossref_primary_10_1016_j_sigpro_2021_108109 crossref_primary_10_1214_20_AOS1980 crossref_primary_10_1016_j_acha_2012_04_002 crossref_primary_10_1109_TVT_2017_2693384 crossref_primary_10_1007_s11222_015_9567_4 crossref_primary_10_1088_1742_6596_1237_3_032059 crossref_primary_10_1137_100799988 crossref_primary_10_1093_imaiai_iaad033 crossref_primary_10_1214_22_EJS2015 crossref_primary_10_1109_TITS_2014_2305334 crossref_primary_10_1109_TPAMI_2020_3046476 crossref_primary_10_1287_ijoc_2022_1251 crossref_primary_10_1002_sta4_296 crossref_primary_10_1080_10618600_2024_2441165 crossref_primary_10_1080_09720502_2015_1040663 crossref_primary_10_1016_j_patcog_2019_06_019 crossref_primary_10_1038_npjqi_2015_18 crossref_primary_10_1109_TIT_2014_2366459 crossref_primary_10_1109_TSP_2017_2755602 crossref_primary_10_1145_1970392_1970395 crossref_primary_10_1007_s10208_011_9084_6 crossref_primary_10_1080_03610926_2020_1843055 crossref_primary_10_1109_TIP_2012_2221729 crossref_primary_10_1016_j_apm_2019_02_001 crossref_primary_10_1109_TSP_2020_2997180 crossref_primary_10_1109_TPAMI_2011_191 crossref_primary_10_3390_rs15010121 crossref_primary_10_1109_TGRS_2014_2321557 crossref_primary_10_1093_imaiai_iaae013 crossref_primary_10_2139_ssrn_4063431 crossref_primary_10_1016_j_dsp_2016_01_006 crossref_primary_10_1109_TNNLS_2023_3236415 crossref_primary_10_1016_j_patcog_2015_09_008 crossref_primary_10_3390_app14104239 crossref_primary_10_1016_j_trc_2024_104513 crossref_primary_10_1080_01431161_2016_1148286 crossref_primary_10_1214_16_EJS1147 crossref_primary_10_1080_01621459_2017_1389740 crossref_primary_10_1190_geo2015_0066_1 crossref_primary_10_1007_s11063_018_9841_5 crossref_primary_10_1016_j_sigpro_2015_02_025 crossref_primary_10_1145_2903716 crossref_primary_10_1109_TPWRS_2023_3237505 crossref_primary_10_1145_3360488 crossref_primary_10_1088_1742_2132_13_5_704 crossref_primary_10_1109_TSP_2020_3011024 crossref_primary_10_1080_10618600_2022_2134873 crossref_primary_10_1109_TIT_2018_2881749 crossref_primary_10_1190_geo2020_0032_1 crossref_primary_10_1007_s11222_020_09939_5 crossref_primary_10_1214_11_AOS894 crossref_primary_10_1007_s10589_017_9898_5 crossref_primary_10_1016_j_sigpro_2014_07_016 crossref_primary_10_1016_j_procs_2016_05_378 crossref_primary_10_1038_s41598_024_63582_y crossref_primary_10_1088_1361_6420_aaf317 crossref_primary_10_1109_TSP_2019_2952057 crossref_primary_10_1109_TSP_2018_2879031 crossref_primary_10_1016_j_procs_2016_05_379 crossref_primary_10_1109_TIT_2012_2204535 crossref_primary_10_1007_s40300_023_00239_2 crossref_primary_10_1016_j_neunet_2017_04_005 crossref_primary_10_1109_MSP_2014_2327238 crossref_primary_10_1287_ijoc_2022_0022 crossref_primary_10_1016_j_sigpro_2014_08_026 crossref_primary_10_1109_TMM_2022_3171088 crossref_primary_10_3390_computers10030033 crossref_primary_10_1109_TNNLS_2022_3215983 crossref_primary_10_1016_j_patcog_2017_10_014 crossref_primary_10_1109_TAC_2021_3135361 crossref_primary_10_1088_0266_5611_26_11_115009 crossref_primary_10_1002_ange_201409291 crossref_primary_10_1109_TIT_2011_2111771 crossref_primary_10_3390_s23104847 crossref_primary_10_1177_0161734620910163 crossref_primary_10_1287_ijoc_2022_1219 crossref_primary_10_1109_LSP_2021_3116525 crossref_primary_10_1016_j_artmed_2018_12_006 crossref_primary_10_1007_s13042_024_02480_1 crossref_primary_10_1016_j_sigpro_2014_08_032 crossref_primary_10_3390_jimaging7070110 crossref_primary_10_1002_sam_11700 crossref_primary_10_1109_TVT_2011_2118777 crossref_primary_10_1007_s11760_019_01482_9 crossref_primary_10_1109_TMM_2016_2613824 crossref_primary_10_1109_TVT_2022_3169404 crossref_primary_10_1214_22_BA1317 crossref_primary_10_1109_TSG_2020_2968814 crossref_primary_10_1214_19_AOS1854 crossref_primary_10_1214_19_AOS1855 crossref_primary_10_1080_02331934_2019_1678157 crossref_primary_10_1109_LGRS_2014_2327224 crossref_primary_10_1109_TIT_2024_3450870 crossref_primary_10_1109_LSP_2017_2708750 crossref_primary_10_1080_03081087_2019_1631246 crossref_primary_10_1109_TSG_2019_2944986 crossref_primary_10_1111_rssb_12550 crossref_primary_10_1214_21_AOS2125 crossref_primary_10_3724_SP_J_1249_2019_05473 crossref_primary_10_1109_TSP_2014_2340820 crossref_primary_10_1137_19M126476X crossref_primary_10_1287_opre_2021_2193 crossref_primary_10_3150_12_BEJ487 crossref_primary_10_1007_s11227_018_2486_3 crossref_primary_10_1007_s11276_020_02328_w crossref_primary_10_1016_j_neucom_2018_02_002 crossref_primary_10_1016_j_comnet_2014_02_020 crossref_primary_10_1109_ACCESS_2022_3177592 crossref_primary_10_1109_LSP_2012_2188026 crossref_primary_10_1073_pnas_1705490115 crossref_primary_10_1109_TWC_2020_3020191 crossref_primary_10_1109_TCSVT_2023_3275299 crossref_primary_10_1186_s13634_020_00698_z crossref_primary_10_1007_s11760_017_1110_y crossref_primary_10_1111_coin_12372 crossref_primary_10_1109_JSTARS_2019_2891114 crossref_primary_10_1109_JSEN_2018_2866686 crossref_primary_10_1109_TIP_2017_2718183 crossref_primary_10_1109_TSP_2016_2586753 crossref_primary_10_1137_110845768 crossref_primary_10_1214_23_AOS2293 crossref_primary_10_1109_TSP_2019_2940121 crossref_primary_10_1007_s11135_023_01659_y crossref_primary_10_1109_TNET_2015_2417809 crossref_primary_10_1109_TCBB_2015_2459692 crossref_primary_10_1016_j_apacoust_2020_107681 crossref_primary_10_1109_TCOMM_2023_3279403 crossref_primary_10_1109_TSP_2015_2440187 crossref_primary_10_1111_bmsp_12340 crossref_primary_10_1109_TAC_2016_2595761 crossref_primary_10_1155_2014_763469 crossref_primary_10_1109_TIP_2017_2698920 crossref_primary_10_1109_TCBB_2020_3027444 crossref_primary_10_1109_TSP_2019_2932875 crossref_primary_10_1016_j_cam_2010_06_010 crossref_primary_10_1109_TSP_2015_2441042 crossref_primary_10_1109_TGRS_2020_3018315 crossref_primary_10_1137_100785028 crossref_primary_10_1109_TPAMI_2024_3512458 crossref_primary_10_1109_TAP_2024_3454456 crossref_primary_10_3390_math11051155 crossref_primary_10_1145_2601408 crossref_primary_10_1214_18_STS642 crossref_primary_10_1109_TIT_2020_3019569 crossref_primary_10_1109_JSTARS_2019_2906360 crossref_primary_10_1109_TPAMI_2017_2734888 crossref_primary_10_1109_TSP_2019_2944758 crossref_primary_10_1364_JOSAA_381158 crossref_primary_10_1016_j_sigpro_2022_108640 crossref_primary_10_1016_j_dsp_2020_102880 crossref_primary_10_1109_TIT_2023_3266271 crossref_primary_10_1109_TSP_2024_3388372 crossref_primary_10_1007_s11760_024_03353_4 crossref_primary_10_1109_JSTSP_2018_2840481 crossref_primary_10_1016_j_jeconom_2020_08_002 crossref_primary_10_1002_widm_1108 crossref_primary_10_1109_TSP_2020_3020397 crossref_primary_10_1137_18M1189464 crossref_primary_10_1145_2822877 crossref_primary_10_1007_s10898_018_0684_4 crossref_primary_10_1109_TCSVT_2011_2106251 crossref_primary_10_1137_110820361 crossref_primary_10_1109_TSP_2015_2500192 crossref_primary_10_1016_j_neucom_2023_01_030 crossref_primary_10_1109_TMI_2017_2744663 crossref_primary_10_1109_TSP_2017_2784361 crossref_primary_10_1016_j_ins_2020_03_103 crossref_primary_10_1145_3478105 crossref_primary_10_1021_acsphotonics_0c00553 crossref_primary_10_1109_JSTSP_2016_2547860 crossref_primary_10_1109_TSP_2018_2813332 crossref_primary_10_1109_TSP_2019_2944740 crossref_primary_10_1287_opre_2021_2182 crossref_primary_10_1109_TSP_2012_2208634 crossref_primary_10_1109_TIT_2023_3345902 crossref_primary_10_1073_pnas_1910053116 crossref_primary_10_1137_23M1580164 crossref_primary_10_1016_j_neucom_2020_05_026 crossref_primary_10_1109_TSP_2020_2988784 crossref_primary_10_1109_TII_2019_2937876 crossref_primary_10_2139_ssrn_4086999 crossref_primary_10_1145_3634751 crossref_primary_10_1109_TSP_2013_2287673 crossref_primary_10_1109_TPAMI_2019_2937869 crossref_primary_10_1137_21M1433812 crossref_primary_10_1109_JSTSP_2016_2555482 crossref_primary_10_1109_ACCESS_2019_2936619 crossref_primary_10_1109_TIP_2014_2329449 crossref_primary_10_1016_j_jvcir_2016_11_005 crossref_primary_10_3390_s21031016 crossref_primary_10_1007_s00034_019_01093_2 crossref_primary_10_1109_TIP_2016_2585047 crossref_primary_10_1007_s11749_024_00934_w
Cites_doi	10.1145/1273496.1273499 10.1007/BF00129684 10.1109/9.554402 10.1007/BFb0030287 10.1090/S0894-0347-08-00600-0 10.1109/TAP.1986.1143830 10.1073/pnas.0709842104 10.1145/138859.138867 10.1109/TIT.2005.862083 10.1109/TSP.2002.1003065 10.1137/090750688 10.1137/070697835 10.1137/090755436 10.1109/TPAMI.2004.52 10.1145/1149283.1149286 10.1109/ACSSC.2008.5074571 10.1007/s10208-009-9045-5 10.1137/080738970 10.1109/TIT.2005.858979 10.1002/cpa.20132 10.1109/ISIT.2009.5205567 10.1109/ACC.2003.1243393 10.1145/380752.380859
ContentType	Journal Article
Copyright	Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jun 2010
Copyright_xml	– notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jun 2010
DBID	97E RIA RIE AAYXX CITATION 7SP 8FD L7M F28 FR3 ADTOC UNPAY
DOI	10.1109/JPROC.2009.2035722
DatabaseName	IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Electronics & Communications Abstracts Technology Research Database Advanced Technologies Database with Aerospace ANTE: Abstracts in New Technology & Engineering Engineering Research Database Unpaywall for CDI: Periodical Content Unpaywall
DatabaseTitle	CrossRef Technology Research Database Advanced Technologies Database with Aerospace Electronics & Communications Abstracts Engineering Research Database ANTE: Abstracts in New Technology & Engineering
DatabaseTitleList	Technology Research Database Engineering Research Database
Database_xml	– sequence: 1 dbid: RIE name: IEEE Xplore (NTUSG) url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/ sourceTypes: Publisher – sequence: 2 dbid: UNPAY name: Unpaywall url: https://proxy.k.utb.cz/login?url=https://unpaywall.org/ sourceTypes: Open Access Repository
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering
EISSN	1558-2256
EndPage	936
ExternalDocumentID	oai:authors.library.caltech.edu:18601 2716848551 10_1109_JPROC_2009_2035722 5454406
Genre	orig-research
GroupedDBID	-DZ -~X .DC 0R~ 123 1OL 29P 3EH 4.4 6IK 85S 97E 9M8 AAJGR AAWTH ABAZT ABFSI ABJNI ABQJQ ABVLG ACBEA ACGFS AENEX AETEA AETIX AFOGA AGNAY AGQYO AGSQL AHBIQ AIBXA ALLEH ALMA_UNASSIGNED_HOLDINGS AZLTO BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD FA8 HZ~ H~9 IAAWW IBMZZ ICLAB IDIHD IFIPE IFJZH IPLJI JAVBF LAI M43 MVM O9- OCL RIA RIE RIU RNS TAE TN5 TWZ UDY UHB UKR UQL VOH WHG XJT XOL YNT ZCA ZXP ZY4 ~02 AAYXX CITATION 7SP 8FD L7M RIG F28 FR3 ADTOC UNPAY
ID	FETCH-LOGICAL-c372t-eb991753ae7daba8cff5d6c2731d4091b976b0bb98b663d855267b1f08bc1f1a3
IEDL.DBID	RIE
ISSN	0018-9219 1558-2256
IngestDate	Sun Oct 26 04:11:47 EDT 2025 Wed Oct 01 13:33:25 EDT 2025 Mon Jun 30 05:21:00 EDT 2025 Thu Apr 24 23:07:19 EDT 2025 Wed Oct 01 02:41:00 EDT 2025 Wed Aug 27 02:43:14 EDT 2025
IsDoiOpenAccess	false
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	6
Language	English
License	https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c372t-eb991753ae7daba8cff5d6c2731d4091b976b0bb98b663d855267b1f08bc1f1a3
Notes	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
OpenAccessLink	https://proxy.k.utb.cz/login?url=https://resolver.caltech.edu/CaltechAUTHORS:20100608-084826169
PQID	1027190402
PQPubID	85453
PageCount	12
ParticipantIDs	unpaywall_primary_10_1109_jproc_2009_2035722 ieee_primary_5454406 crossref_citationtrail_10_1109_JPROC_2009_2035722 crossref_primary_10_1109_JPROC_2009_2035722 proquest_journals_1027190402 proquest_miscellaneous_1671231787
ProviderPackageCode	CITATION AAYXX
PublicationCentury	2000
PublicationDate	2010-06-01
PublicationDateYYYYMMDD	2010-06-01
PublicationDate_xml	– month: 06 year: 2010 text: 2010-06-01 day: 01
PublicationDecade	2010
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	Proceedings of the IEEE
PublicationTitleAbbrev	JPROC
PublicationYear	2010
Publisher	IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml	– name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References	ref34 ref12 ref15 ref31 ref30 ref33 ref11 ref32 ref10 ref17 fazel (ref19) 2002 (ref2) 2008; 25 ref16 ref18 (ref1) 0 weng (ref35) 0 ref24 cands (ref13) 2007; 35 ref23 ref26 cai (ref9) 2008 ref20 ref21 ma (ref27) 2008 ref28 ref29 ref8 ref7 ref3 keshavan (ref25) 2009 ref5 gilbert (ref22) 2005 argyriou (ref4) 2007 beck (ref6) 1998 cands (ref14) 2009
References_xml	– volume: 25 year: 2008 ident: ref2 publication-title: IEEE Signal Processing Mag (Special Issue on Sensing Sampling and Compression) – ident: ref3 doi: 10.1145/1273496.1273499 – ident: ref33 doi: 10.1007/BF00129684 – ident: ref28 doi: 10.1109/9.554402 – ident: ref16 doi: 10.1007/BFb0030287 – year: 1998 ident: ref6 article-title: computational study and comparisons of lft reducibility methods publication-title: Proc Amer Contr Conf – ident: ref18 doi: 10.1090/S0894-0347-08-00600-0 – ident: ref30 doi: 10.1109/TAP.1986.1143830 – year: 2008 ident: ref9 publication-title: A Singular Value Thresholding Algorithm for Matrix Completion – ident: ref31 doi: 10.1073/pnas.0709842104 – ident: ref23 doi: 10.1145/138859.138867 – year: 2009 ident: ref14 publication-title: The power of convex relaxation Near-optimal matrix completion – ident: ref11 doi: 10.1109/TIT.2005.862083 – year: 0 ident: ref1 – ident: ref34 doi: 10.1109/TSP.2002.1003065 – ident: ref32 doi: 10.1137/090750688 – ident: ref29 doi: 10.1137/070697835 – year: 2005 ident: ref22 article-title: improved time bounds for near-optimal sparse fourier representation publication-title: Proc Wavelets XI SPIE Opt Photon – ident: ref26 doi: 10.1137/090755436 – volume: 35 year: 2007 ident: ref13 article-title: the dantzig selector: statistical estimation when <tex notation="tex">$p$</tex> is much larger than <tex notation="tex">$n$</tex> publication-title: Ann Statist – ident: ref15 doi: 10.1109/TPAMI.2004.52 – year: 2002 ident: ref19 publication-title: Matrix Rank Minimization With Applications – ident: ref7 doi: 10.1145/1149283.1149286 – ident: ref20 doi: 10.1109/ACSSC.2008.5074571 – ident: ref10 doi: 10.1007/s10208-009-9045-5 – year: 0 ident: ref35 article-title: matrix completion for doa estimation – ident: ref8 doi: 10.1137/080738970 – year: 2008 ident: ref27 publication-title: Fixed Point and Bregman Iterative Methods for Matrix Rank Minimization – ident: ref12 doi: 10.1109/TIT.2005.858979 – ident: ref17 doi: 10.1002/cpa.20132 – year: 2007 ident: ref4 article-title: multi-task feature learning publication-title: Neural Inf Process Syst – year: 2009 ident: ref25 publication-title: Matrix completion from noisy entries – ident: ref24 doi: 10.1109/ISIT.2009.5205567 – ident: ref21 doi: 10.1109/ACC.2003.1243393 – ident: ref5 doi: 10.1145/380752.380859
SSID	ssj0003563
Score	2.5799944
Snippet	On the heels of compressed sensing, a new field has very recently emerged. This field addresses a broad range of problems of significant practical interest,...
SourceID	unpaywall proquest crossref ieee
SourceType	Open Access Repository Aggregation Database Enrichment Source Index Database Publisher
StartPage	925
SubjectTerms	Collaboration Compressed Compressed sensing Computer vision Detection duality in optimization Filtering Frequency Linear matrix inequalities low-rank matrices Machine learning Matrices matrix completion Minimization Motion pictures Noise Noise level nuclear-norm minimization Optimization oracle inequalities Quantitative analysis Remote sensing semidefinite programming Studies
SummonAdditionalLinks	– databaseName: Unpaywall dbid: UNPAY link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dT9tADLdGeRg8wBhMy1ZQkPa2Be6uuVyON1SBKiQKYqsGT9F9RXSrEgSpBvz18yVpRTcJCd4ixYmc2Gf_fD7bAF-cEoRroSOlJYli7XqRQk8eWUNyGdtcGu6rkU-HyWAUn1zyy3bDzdfCYIxZTurmqD5b3Oy27feba5TY4Ozi-4FP4JLEp-3TGNExTeQSLCccsXgHlkfD88OrxvziSmb1ZA_0magO6NxnVTNE7v_yDqLpV8lIjwvGFjxTPWplAXW-nRY36uGPmkyeOKDjdchmrDfnTn7vTSu9Zx7_6er4-m97B2stNg0PG2XagDeueA-rTzoWbkL31Lf0vw-9GfFtu8si_DmursNhOb5zWzA6PvrRH0TtgIXI9ASrIqcRHWK8opywSqvU5Dm3iUFEQy3GfVQjVtFEa5lqBCY25ZwlQtOcpNrQnKreB-gUZeE-Qsisr94Sitg0RrNg0zxmiqbEcOdDHBkAnf3czLTdx_0QjElWRyFEZifnF2d9PxVTZq1AAvg6f-am6b3xLPWml9mcEqEhcpIE0J3JMGuX5x2-hQlEQhg7B7A7v40Ly2dLVOHKKdIkAr06RYMWwLe57P9jpNajBUY-vYz8M6w0JxL8zk4XOtXt1G0j0Kn0TqvNfwHTU_LO priority: 102 providerName: Unpaywall
Title	Matrix Completion With Noise
URI	https://ieeexplore.ieee.org/document/5454406 https://www.proquest.com/docview/1027190402 https://www.proquest.com/docview/1671231787 https://resolver.caltech.edu/CaltechAUTHORS:20100608-084826169
UnpaywallVersion	submittedVersion
Volume	98
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVIEE databaseName: IEEE Xplore (NTUSG) customDbUrl: eissn: 1558-2256 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0003563 issn: 1558-2256 databaseCode: RIE dateStart: 19630101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE
link	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1ZS8NAEB48HtQHbzFaJYJvmrqbJtnksRRFhFYRi_oU9goeJRFN8Pj1ziZpsCriSwhkEiazx3yzu_MNwL7mjPiCCYeLiDie0B2Hoyd3lCRJ5Kkkkr7JRu4PgtOhd3bj30zBYZMLo7UuD5_ptrkt9_JVJguzVHaE3t7zDL_2NAuDKlermXU7fl01jeIAxmE4TpAh0dHZxeV5r6KmdFGOue6EEyqrqkwAzLkifeLvr3w0-uJrTpagP9ayOmLy2C5y0ZYf3wgc__sby7BYg067W_WSFZjS6SosfKEiXINW33D1v9lmfjB83FlqX9_nd_Ygu3_R6zA8Ob7qnTp15QRHdpibO1og7MNAhGumuOChTBJfBRKhClUY0FGBIEQQIaJQIOJQoe-7ARM0IaGQNKG8swEzaZbqTbBdZdKyGCcqRKXxmngupyGRvjaxS2QBHZsyljWtuKluMYrL8IJEcWl-U-4yimvzW3DQvPNUkWr8Kb1mbNhI1uazoDVusbgedy_4FZchxMGg2IK95jGOGLMNwlOdFSgTMHTXFGcqCw6blv6hyINBEBOKbP2uyDbMV0cKzNJMC2by50LvIFLJxW7ZRXdhdji46N5-Aq3p4qQ
linkProvider	IEEE
linkToHtml	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3dT9swED8heCg8AONDy1ZYkPYGKXYa18kjqqg6aMuEQPAW-SuCUSVoTTTYX79zkkYtm9Bekki5RJdz7Pud7fsdwFcjOGGSS0_IiHiBNF1PoCf3tCJJFOgkUsxmI48nveFtcHHP7lfgpMmFMcaUm89Mx16Wa_k6U4WdKjtFbx8Ell97Dc8Bq7K1mnG3y-q6aRS7MHbEeYoMiU4vvl9f9StySh_luO8vuaGyrsoSxGwV6bN4_SWm0wVvM9iC8VzPapPJU6fIZUf9fkPh-L8fsg2bNex0z6r_5AOsmHQHNhbICHehPbZs_S-uHSEsI3eWuneP-YM7yR5nZg9uB-c3_aFX107wVJf7uWckAj8MRYThWkgRqiRhuqcQrFCNIR2VCEMkkTIKJWIOHTLm97ikCQmlogkV3X1YTbPUfATX1zYxiwuiQ1Qaj0ngCxoSxYyNXiIH6NyUsaqJxW19i2lcBhgkikvz24KXUVyb34Hj5pnnilbjXelda8NGsjafA-15i8V1z5vhW3yOIAfDYgeOmtvYZ-xCiEhNVqBMj6PDpjhWOXDStPRfivywGGJJkU__VuQLtIY341E8-ja5_Azr1QYDO1HThtX8Z2EOELfk8rD8Xf8AlJbkQQ
linkToUnpaywall	http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dT9tADLdGeRg8wBhMy1ZQkPa2Be6uuVyON1SBKiQKYqsGT9F9RXSrEgSpBvz18yVpRTcJCd4ixYmc2Gf_fD7bAF-cEoRroSOlJYli7XqRQk8eWUNyGdtcGu6rkU-HyWAUn1zyy3bDzdfCYIxZTurmqD5b3Oy27feba5TY4Ozi-4FP4JLEp-3TGNExTeQSLCccsXgHlkfD88OrxvziSmb1ZA_0magO6NxnVTNE7v_yDqLpV8lIjwvGFjxTPWplAXW-nRY36uGPmkyeOKDjdchmrDfnTn7vTSu9Zx7_6er4-m97B2stNg0PG2XagDeueA-rTzoWbkL31Lf0vw-9GfFtu8si_DmursNhOb5zWzA6PvrRH0TtgIXI9ASrIqcRHWK8opywSqvU5Dm3iUFEQy3GfVQjVtFEa5lqBCY25ZwlQtOcpNrQnKreB-gUZeE-Qsisr94Sitg0RrNg0zxmiqbEcOdDHBkAnf3czLTdx_0QjElWRyFEZifnF2d9PxVTZq1AAvg6f-am6b3xLPWml9mcEqEhcpIE0J3JMGuX5x2-hQlEQhg7B7A7v40Ly2dLVOHKKdIkAr06RYMWwLe57P9jpNajBUY-vYz8M6w0JxL8zk4XOtXt1G0j0Kn0TqvNfwHTU_LO
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Matrix+Completion+With+Noise&rft.jtitle=Proceedings+of+the+IEEE&rft.au=Candes%2C+Emmanuel+J.&rft.au=Plan%2C+Yaniv&rft.date=2010-06-01&rft.pub=IEEE&rft.issn=0018-9219&rft.volume=98&rft.issue=6&rft.spage=925&rft.epage=936&rft_id=info:doi/10.1109%2FJPROC.2009.2035722&rft.externalDocID=5454406
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9219&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9219&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9219&client=summon