AMP-Inspired Deep Networks for Sparse Linear Inverse Problems

Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem, where one seeks to recover a sparse signal from a few noisy linear measurements. In this paper, we propose two novel...

Full description

Saved in:

Bibliographic Details
Published in:	IEEE transactions on signal processing Vol. 65; no. 16; pp. 4293 - 4308
Main Authors:	Borgerding, Mark, Schniter, Philip, Rangan, Sundeep
Format:	Journal Article
Language:	English
Published:	IEEE 15.08.2017
Subjects:	approximate message passing Approximation algorithms compressive sensing Deep learning Inverse problems Machine learning massive MIMO Message passing Probability density function random access Signal processing algorithms Transforms
ISSN:	1053-587X, 1941-0476
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem, where one seeks to recover a sparse signal from a few noisy linear measurements. In this paper, we propose two novel neural-network architectures that decouple prediction errors across layers in the same way that the approximate message passing (AMP) algorithms decouple them across iterations: through Onsager correction. First, we propose a "learned AMP" network that significantly improves upon Gregor and LeCun's "learned ISTA." Second, inspired by the recently proposed "vector AMP" (VAMP) algorithm, we propose a "learned VAMP" network that offers increased robustness to deviations in the measurement matrix from i.i.d. Gaussian. In both cases, we jointly learn the linear transforms and scalar nonlinearities of the network. Interestingly, with i.i.d. signals, the linear transforms and scalar nonlinearities prescribed by the VAMP algorithm coincide with the values learned through back-propagation, leading to an intuitive interpretation of learned VAMP. Finally, we apply our methods to two problems from 5G wireless communications: compressive random access and massive-MIMO channel estimation.
AbstractList	Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem, where one seeks to recover a sparse signal from a few noisy linear measurements. In this paper, we propose two novel neural-network architectures that decouple prediction errors across layers in the same way that the approximate message passing (AMP) algorithms decouple them across iterations: through Onsager correction. First, we propose a "learned AMP" network that significantly improves upon Gregor and LeCun's "learned ISTA." Second, inspired by the recently proposed "vector AMP" (VAMP) algorithm, we propose a "learned VAMP" network that offers increased robustness to deviations in the measurement matrix from i.i.d. Gaussian. In both cases, we jointly learn the linear transforms and scalar nonlinearities of the network. Interestingly, with i.i.d. signals, the linear transforms and scalar nonlinearities prescribed by the VAMP algorithm coincide with the values learned through back-propagation, leading to an intuitive interpretation of learned VAMP. Finally, we apply our methods to two problems from 5G wireless communications: compressive random access and massive-MIMO channel estimation.
Author	Schniter, Philip Borgerding, Mark Rangan, Sundeep
Author_xml	– sequence: 1 givenname: Mark surname: Borgerding fullname: Borgerding, Mark email: borgerding.7@osu.edu organization: Dept. of Electr. & Comput. Eng., Ohio State Univ., Columbus, OH, USA – sequence: 2 givenname: Philip surname: Schniter fullname: Schniter, Philip email: schniter.1@osu.edu organization: Dept. of Electr. & Comput. Eng., Ohio State Univ., Columbus, OH, USA – sequence: 3 givenname: Sundeep surname: Rangan fullname: Rangan, Sundeep email: srangan@nyu.edu organization: Dept. of Electr. & Comput. Eng., New York Univ., New York, NY, USA
BookMark	eNp9j0tLw0AUhQepYFvdC27yB1LvZCbzWLgo9RWoWmgFd2EyuQOjbRJmguK_t6HFhQtX99zFdw7fhIyatkFCLinMKAV9vVmvZhlQOcskKOBwQsZUc5oCl2K0z5CzNFfy7YxMYnwHoJxrMSY386dVWjSx8wHr5BaxS56x_2rDR0xcG5J1Z0LEZOkbNCEpmk8c3lVoqy3u4jk5dWYb8eJ4p-T1_m6zeEyXLw_FYr5MbSZYn6JiyrEaLeOVhVrXvKKobW4sCkO1yxxDpTMlgdnKWlVTWelcKldpqKlzbErg0GtDG2NAV3bB70z4LimUg3651y8H_fKov0fEH8T63vS-bfpg_PY_8OoAekT83ZGacRCC_QCkOGoR
CODEN	ITPRED
CitedBy_id	crossref_primary_10_1109_JSYST_2022_3175658 crossref_primary_10_1109_JSAC_2021_3087243 crossref_primary_10_1109_TGRS_2020_2982490 crossref_primary_10_3390_rs15174126 crossref_primary_10_1109_TIT_2019_2947487 crossref_primary_10_1109_JSAC_2020_3036959 crossref_primary_10_1109_ACCESS_2020_2974479 crossref_primary_10_1093_jge_gxac041 crossref_primary_10_1109_TSP_2023_3334396 crossref_primary_10_1109_JSEN_2021_3090948 crossref_primary_10_1109_LWC_2024_3361916 crossref_primary_10_1109_TPAMI_2021_3125041 crossref_primary_10_1109_TMC_2022_3207164 crossref_primary_10_1109_TWC_2024_3380638 crossref_primary_10_1109_TWC_2024_3376381 crossref_primary_10_1109_TGRS_2022_3165541 crossref_primary_10_1109_LCOMM_2021_3123368 crossref_primary_10_1016_j_eswa_2022_119220 crossref_primary_10_1016_j_dsp_2022_103867 crossref_primary_10_1088_2040_8986_ad08dc crossref_primary_10_1109_TCI_2023_3277629 crossref_primary_10_1109_TGRS_2023_3237660 crossref_primary_10_1109_JSAC_2023_3240781 crossref_primary_10_1109_JIOT_2021_3097133 crossref_primary_10_1121_10_0017882 crossref_primary_10_1109_TSP_2021_3076900 crossref_primary_10_1109_MWC_008_2200157 crossref_primary_10_1109_TCOMM_2020_3031613 crossref_primary_10_1109_TWC_2023_3326952 crossref_primary_10_1109_TWC_2022_3153106 crossref_primary_10_1109_TPAMI_2022_3172214 crossref_primary_10_1109_TIP_2019_2944270 crossref_primary_10_1109_ACCESS_2018_2886471 crossref_primary_10_1109_JSAC_2021_3087269 crossref_primary_10_1016_j_dsp_2020_102680 crossref_primary_10_1109_TCSII_2020_3024912 crossref_primary_10_1109_TPAMI_2024_3406473 crossref_primary_10_1016_j_future_2019_01_041 crossref_primary_10_1109_TWC_2021_3120926 crossref_primary_10_1109_TSP_2019_2912879 crossref_primary_10_1109_JSAC_2021_3078500 crossref_primary_10_1109_TVT_2023_3291693 crossref_primary_10_1002_dac_5400 crossref_primary_10_1109_TIP_2022_3195319 crossref_primary_10_7717_peerj_cs_2582 crossref_primary_10_1109_TAP_2024_3361664 crossref_primary_10_1109_LCOMM_2020_3011571 crossref_primary_10_1088_1742_6596_1607_1_012101 crossref_primary_10_1137_20M1353368 crossref_primary_10_1109_TIP_2022_3211473 crossref_primary_10_1109_TWC_2023_3324679 crossref_primary_10_1109_JSTARS_2020_3014696 crossref_primary_10_1016_j_acha_2024_101719 crossref_primary_10_1109_TGRS_2021_3093307 crossref_primary_10_1007_s11425_023_2293_3 crossref_primary_10_1145_3412360 crossref_primary_10_1109_TSP_2020_3035832 crossref_primary_10_1109_TAES_2023_3235746 crossref_primary_10_3390_jimaging8070178 crossref_primary_10_1016_j_sigpro_2020_107699 crossref_primary_10_1109_TCOMM_2024_3506912 crossref_primary_10_1109_TWC_2021_3067903 crossref_primary_10_1109_TVT_2023_3323677 crossref_primary_10_1109_TGRS_2023_3268132 crossref_primary_10_1109_MWC_001_1900491 crossref_primary_10_3390_s22103938 crossref_primary_10_1137_23M1625846 crossref_primary_10_1109_TCOMM_2022_3218630 crossref_primary_10_1109_TVT_2021_3111081 crossref_primary_10_1109_TGRS_2021_3110579 crossref_primary_10_1016_j_sigpro_2023_109198 crossref_primary_10_1109_LWC_2022_3200123 crossref_primary_10_3390_rs15225320 crossref_primary_10_1109_TSP_2018_2873548 crossref_primary_10_1016_j_knosys_2023_110963 crossref_primary_10_1109_LCOMM_2021_3116878 crossref_primary_10_1109_TSP_2023_3272286 crossref_primary_10_1109_JSAC_2022_3143260 crossref_primary_10_3390_s21196551 crossref_primary_10_1109_TCI_2024_3507645 crossref_primary_10_1109_TIP_2021_3078058 crossref_primary_10_1002_dac_6007 crossref_primary_10_3390_app10175909 crossref_primary_10_1109_ACCESS_2020_3029518 crossref_primary_10_1109_JIOT_2020_3021724 crossref_primary_10_1109_LCOMM_2020_2974199 crossref_primary_10_1109_JSEN_2020_3025053 crossref_primary_10_1109_LSP_2019_2929869 crossref_primary_10_1109_TCOMM_2023_3294957 crossref_primary_10_1109_TWC_2020_3026471 crossref_primary_10_1109_JIOT_2025_3555802 crossref_primary_10_3390_rs13214429 crossref_primary_10_1109_TSP_2022_3143372 crossref_primary_10_1109_ACCESS_2019_2942204 crossref_primary_10_3390_s21041442 crossref_primary_10_1109_TWC_2020_3033334 crossref_primary_10_1109_TGRS_2021_3073123 crossref_primary_10_1109_TWC_2022_3187790 crossref_primary_10_1109_TIM_2025_3588970 crossref_primary_10_1109_TVT_2018_2883669 crossref_primary_10_1109_JSAC_2021_3087233 crossref_primary_10_1109_TWC_2022_3145399 crossref_primary_10_1016_j_phycom_2023_102018 crossref_primary_10_1109_TIP_2020_3044472 crossref_primary_10_1109_COMST_2023_3300664 crossref_primary_10_1109_LGRS_2024_3367717 crossref_primary_10_1109_TIP_2021_3104168 crossref_primary_10_1016_j_neunet_2022_11_011 crossref_primary_10_1109_TIP_2020_3014729 crossref_primary_10_1007_s10915_023_02315_1 crossref_primary_10_1088_1361_6420_ad9d73 crossref_primary_10_1109_LCOMM_2020_2989672 crossref_primary_10_1109_LWC_2021_3069199 crossref_primary_10_1109_COMST_2023_3315374 crossref_primary_10_1109_TWC_2023_3327995 crossref_primary_10_3390_rs15010013 crossref_primary_10_1109_TWC_2023_3258405 crossref_primary_10_1109_TGRS_2021_3111901 crossref_primary_10_1109_TSP_2022_3207269 crossref_primary_10_1109_TCCN_2023_3247756 crossref_primary_10_1007_s11277_025_11767_7 crossref_primary_10_1109_LCOMM_2020_3045763 crossref_primary_10_1109_LSP_2022_3188446 crossref_primary_10_1109_TWC_2022_3186084 crossref_primary_10_1088_1742_5468_ab321a crossref_primary_10_1016_j_icte_2021_03_011 crossref_primary_10_1109_TWC_2023_3330816 crossref_primary_10_1109_TIM_2022_3154803 crossref_primary_10_3390_acoustics4040050 crossref_primary_10_1109_TGRS_2022_3177927 crossref_primary_10_1109_ACCESS_2021_3118608 crossref_primary_10_1214_21_AOS2101 crossref_primary_10_1109_TSP_2020_2976585 crossref_primary_10_1109_TCI_2023_3315853 crossref_primary_10_1049_tje2_12120 crossref_primary_10_1162_neco_a_01715 crossref_primary_10_1109_TWC_2023_3271521 crossref_primary_10_1109_TCI_2019_2892123 crossref_primary_10_1109_TSP_2021_3086593 crossref_primary_10_1109_ACCESS_2020_3035726 crossref_primary_10_1109_TGRS_2025_3560140 crossref_primary_10_3390_rs14143472 crossref_primary_10_1109_TSP_2024_3510623 crossref_primary_10_1109_JIOT_2025_3542398 crossref_primary_10_1016_j_dsp_2025_105287 crossref_primary_10_1109_TGRS_2021_3068405 crossref_primary_10_1109_COMST_2019_2904897 crossref_primary_10_1109_LCOMM_2022_3208031 crossref_primary_10_1109_COMST_2023_3326399 crossref_primary_10_1109_LGRS_2024_3509520 crossref_primary_10_1109_MWC_2019_1900027 crossref_primary_10_1109_JSAC_2021_3126071 crossref_primary_10_1109_TCOMM_2020_3027027 crossref_primary_10_1109_JIOT_2022_3163593 crossref_primary_10_1109_TIP_2021_3091834 crossref_primary_10_1109_TNNLS_2021_3093818 crossref_primary_10_1002_stc_2979 crossref_primary_10_1109_TCI_2022_3181473 crossref_primary_10_1109_ACCESS_2021_3064927 crossref_primary_10_1109_TWC_2025_3563104 crossref_primary_10_1016_j_dsp_2020_102862 crossref_primary_10_3390_s22155533 crossref_primary_10_1016_j_image_2018_03_017 crossref_primary_10_1109_TSP_2020_2978615 crossref_primary_10_1109_LWC_2021_3123579 crossref_primary_10_1109_LCOMM_2024_3371105 crossref_primary_10_1109_ACCESS_2020_2978237 crossref_primary_10_1109_MCOM_004_2200164 crossref_primary_10_1016_j_neucom_2022_08_034 crossref_primary_10_1109_TSP_2024_3381749 crossref_primary_10_1109_TGRS_2022_3205628 crossref_primary_10_1016_j_sigpro_2020_107729 crossref_primary_10_1109_TVT_2020_2977733 crossref_primary_10_1109_TWC_2021_3133296 crossref_primary_10_1016_j_hspr_2024_11_007 crossref_primary_10_3390_a16010060 crossref_primary_10_1007_s11432_021_3470_1 crossref_primary_10_1109_ACCESS_2021_3128721 crossref_primary_10_1109_JSTSP_2020_2977507 crossref_primary_10_3390_app11178117 crossref_primary_10_1088_1361_6501_acfb2a crossref_primary_10_1109_TIT_2021_3077471 crossref_primary_10_3390_rs17071253 crossref_primary_10_54097_p90khg63 crossref_primary_10_1109_JIOT_2018_2876152 crossref_primary_10_1109_TCI_2022_3233185 crossref_primary_10_3390_rs14153509 crossref_primary_10_1109_JSAC_2022_3191124 crossref_primary_10_1109_TWC_2021_3100500 crossref_primary_10_1109_ACCESS_2023_3293637 crossref_primary_10_1109_TCOMM_2024_3440875 crossref_primary_10_1109_ACCESS_2024_3447652 crossref_primary_10_1109_TIP_2021_3069296 crossref_primary_10_1109_TWC_2023_3296218 crossref_primary_10_1007_s10851_019_00889_w crossref_primary_10_1109_MGRS_2024_3494754 crossref_primary_10_1007_s10462_022_10259_5 crossref_primary_10_1109_TIT_2025_3535923 crossref_primary_10_1109_TITS_2020_3009223 crossref_primary_10_1109_TWC_2023_3328437 crossref_primary_10_1109_TWC_2024_3416375 crossref_primary_10_1016_j_hcc_2023_100125 crossref_primary_10_1109_ACCESS_2021_3057621
Cites_doi	10.1109/79.799930 10.1109/ICASSP.2017.7952957 10.1109/TIT.2009.2016018 10.1109/ICASSP.2015.7178325 10.1109/ITWKSPS.2010.5503193 10.1137/080716542 10.1109/ISIT.2009.5205769 10.1214/14-AAP1010 10.1111/j.2517-6161.1996.tb02080.x 10.1109/LSP.2016.2548245 10.1002/ett.2633 10.1109/ACSSC.2016.7869633 10.1002/cpa.20042 10.1109/CVPR.2014.349 10.1109/ALLERTON.2015.7447163 10.1109/CVPR.2016.55 10.1109/ISIT.2017.8006899 10.1109/TWC.2014.2365813 10.1109/TPAMI.2015.2439281 10.1109/TSP.2014.2386294 10.1137/S1064827596304010 10.1109/TSP.2015.2408569 10.1109/CVPR.2013.142 10.1109/TSP.2012.2217334 10.1109/GlobalSIP.2016.7905837 10.1017/CBO9780511794308.010 10.1109/TSP.2002.803324 10.1109/TIT.2013.2250578 10.1109/TSP.2013.2272287 10.1109/JSAC.2014.2328098 10.1109/ICASSP.2017.7952561 10.1109/CVPR.2012.6247952 10.1017/CBO9780511794308 10.1109/83.661182 10.1002/cpa.20124 10.1109/ACCESS.2015.2407194 10.1109/ISIT.2011.6033942 10.1109/ICCV.2015.50 10.1109/MSP.2011.2178495 10.1109/TIT.2010.2094817 10.1073/pnas.0909892106
ContentType	Journal Article
DBID	97E RIA RIE AAYXX CITATION
DOI	10.1109/TSP.2017.2708040
DatabaseName	IEEE All-Society Periodicals Package (ASPP) 2005-present IEEE All-Society Periodicals Package (ASPP) 1998-Present IEEE Electronic Library (IEL) CrossRef
DatabaseTitle	CrossRef
DatabaseTitleList
Database_xml	– sequence: 1 dbid: RIE name: IEEE/IET Electronic Library url: https://ieeexplore.ieee.org/ sourceTypes: Publisher
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering
EISSN	1941-0476
EndPage	4308
ExternalDocumentID	10_1109_TSP_2017_2708040 7934066
Genre	orig-research
GrantInformation_xml	– fundername: National Science Foundation grantid: 1527162; 1539960; 1302336; 1547332; 1564142 funderid: 10.13039/100000001
GroupedDBID	-~X .DC 0R~ 29I 4.4 5GY 6IK 85S 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACIWK ACNCT AENEX AGQYO AHBIQ AJQPL AKJIK AKQYR ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 EBS EJD F5P HZ~ IFIPE IPLJI JAVBF LAI MS~ O9- OCL P2P RIA RIE RNS TAE TN5 AAYXX CITATION
ID	FETCH-LOGICAL-c263t-e838f3dec34bc0d9d4b1e9c5ace6a19f2f3e8928703cbcc8d17b9578fb90d1ff3
IEDL.DBID	RIE
ISICitedReferencesCount	322
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000404286900011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	1053-587X
IngestDate	Sat Nov 29 07:53:59 EST 2025 Tue Nov 18 21:09:03 EST 2025 Tue Aug 26 17:00:18 EDT 2025
IsPeerReviewed	true
IsScholarly	true
Issue	16
Language	English
License	https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html https://doi.org/10.15223/policy-029 https://doi.org/10.15223/policy-037
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c263t-e838f3dec34bc0d9d4b1e9c5ace6a19f2f3e8928703cbcc8d17b9578fb90d1ff3
PageCount	16
ParticipantIDs	crossref_primary_10_1109_TSP_2017_2708040 ieee_primary_7934066 crossref_citationtrail_10_1109_TSP_2017_2708040
PublicationCentury	2000
PublicationDate	2017-Aug.15,-15 2017-8-15
PublicationDateYYYYMMDD	2017-08-15
PublicationDate_xml	– month: 08 year: 2017 text: 2017-Aug.15,-15 day: 15
PublicationDecade	2010
PublicationTitle	IEEE transactions on signal processing
PublicationTitleAbbrev	TSP
PublicationYear	2017
Publisher	IEEE
Publisher_xml	– name: IEEE
References	ref53 ref52 ref11 ref54 ref10 abadi (ref40) 2015 ref17 gregor (ref4) 2010 ref19 ref18 goodfellow (ref3) 2016 ref51 ref50 xin (ref32) 2016 ref46 ref45 ref48 ref47 ref42 ref44 ref43 ref49 ref7 kingma (ref41) 2015 veit (ref14) 2016 ref9 hershey (ref27) 2014 ref6 ref35 ref34 ref37 ref31 ref30 ref33 ref2 wang (ref8) 2016 ref1 ref39 ref38 iliadis (ref36) 2016 tibshirani (ref16) 1996; 58 ref24 ref23 ref26 ref25 ref20 ref22 ref21 srivastava (ref15) 2015 ref28 sprechmann (ref5) 2012 he (ref13) 2015 ref29 rangan (ref12) 2016
References_xml	– ident: ref38 doi: 10.1109/79.799930 – ident: ref25 doi: 10.1109/ICASSP.2017.7952957 – ident: ref46 doi: 10.1109/TIT.2009.2016018 – ident: ref24 doi: 10.1109/ICASSP.2015.7178325 – ident: ref23 doi: 10.1109/ITWKSPS.2010.5503193 – ident: ref10 doi: 10.1137/080716542 – ident: ref44 doi: 10.1109/ISIT.2009.5205769 – ident: ref22 doi: 10.1214/14-AAP1010 – volume: 58 start-page: 267 year: 1996 ident: ref16 article-title: Regression shrinkage and selection via the lasso publication-title: J Roy Statist Soc B doi: 10.1111/j.2517-6161.1996.tb02080.x – ident: ref6 doi: 10.1109/LSP.2016.2548245 – ident: ref45 doi: 10.1002/ett.2633 – ident: ref51 doi: 10.1109/ACSSC.2016.7869633 – ident: ref19 doi: 10.1002/cpa.20042 – ident: ref30 doi: 10.1109/CVPR.2014.349 – ident: ref33 doi: 10.1109/ALLERTON.2015.7447163 – ident: ref34 doi: 10.1109/CVPR.2016.55 – ident: ref49 doi: 10.1109/ISIT.2017.8006899 – ident: ref48 doi: 10.1109/TWC.2014.2365813 – year: 2015 ident: ref40 article-title: TensorFlow: Large-scale machine learning on heterogeneous systems – ident: ref31 doi: 10.1109/TPAMI.2015.2439281 – start-page: 615 year: 2012 ident: ref5 article-title: Learning efficient structured-sparse models publication-title: Proc Int Conf Mach Learn – ident: ref52 doi: 10.1109/TSP.2014.2386294 – ident: ref17 doi: 10.1137/S1064827596304010 – ident: ref37 doi: 10.1109/TSP.2015.2408569 – ident: ref29 doi: 10.1109/CVPR.2013.142 – year: 2016 ident: ref3 publication-title: Deep Learning – start-page: 550 year: 2016 ident: ref14 article-title: Residual networks behave like ensembles of relatively shallow networks publication-title: Proc Neural Inf Process Syst Conf – year: 2016 ident: ref36 article-title: Deep fully-connected networks for video compressive sensing – ident: ref53 doi: 10.1109/TSP.2012.2217334 – start-page: 399 year: 2010 ident: ref4 article-title: Learning fast approximations of sparse coding publication-title: Proc Int Conf Mach Learn – start-page: 2194 year: 2016 ident: ref8 article-title: Learning deep $\ell _0$ encoders publication-title: Proc AAAI Conf Artif Intell – year: 2015 ident: ref41 article-title: Adam: A method for stochastic optimization publication-title: Proc Int Conf Learn Representations – ident: ref1 doi: 10.1109/GlobalSIP.2016.7905837 – ident: ref20 doi: 10.1017/CBO9780511794308.010 – ident: ref54 doi: 10.1109/TSP.2002.803324 – ident: ref26 doi: 10.1109/TIT.2013.2250578 – ident: ref39 doi: 10.1109/TSP.2013.2272287 – year: 2016 ident: ref12 article-title: Vector approximate message passing – ident: ref42 doi: 10.1109/JSAC.2014.2328098 – year: 2014 ident: ref27 article-title: Deep unfolding: Model-based inspiration of novel deep architectures publication-title: Tech Rep – ident: ref35 doi: 10.1109/ICASSP.2017.7952561 – ident: ref28 doi: 10.1109/CVPR.2012.6247952 – ident: ref2 doi: 10.1017/CBO9780511794308 – ident: ref9 doi: 10.1109/83.661182 – ident: ref18 doi: 10.1002/cpa.20124 – ident: ref43 doi: 10.1109/ACCESS.2015.2407194 – ident: ref50 doi: 10.1109/ISIT.2011.6033942 – year: 2015 ident: ref13 article-title: Deep residual learning for image recognition – start-page: 2377 year: 2015 ident: ref15 article-title: Training very deep networks publication-title: Proc Neural Inf Process Syst Conf – ident: ref7 doi: 10.1109/ICCV.2015.50 – start-page: 4340 year: 2016 ident: ref32 article-title: Maximal sparsity from deep networks? publication-title: Proc Neural Inf Process Syst – ident: ref47 doi: 10.1109/MSP.2011.2178495 – ident: ref21 doi: 10.1109/TIT.2010.2094817 – ident: ref11 doi: 10.1073/pnas.0909892106
SSID	ssj0014496
Score	2.6753018
Snippet	Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse...
SourceID	crossref ieee
SourceType	Enrichment Source Index Database Publisher
StartPage	4293
SubjectTerms	approximate message passing Approximation algorithms compressive sensing Deep learning Inverse problems Machine learning massive MIMO Message passing Probability density function random access Signal processing algorithms Transforms
Title	AMP-Inspired Deep Networks for Sparse Linear Inverse Problems
URI	https://ieeexplore.ieee.org/document/7934066
Volume	65
WOSCitedRecordID	wos000404286900011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVIEE databaseName: IEEE/IET Electronic Library customDbUrl: eissn: 1941-0476 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014496 issn: 1053-587X databaseCode: RIE dateStart: 19910101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEF7a4kEPvqpYX-TgRTBtNrvJ7h48FLXowRJohd7CPmZBkLT04e93N0lDDyJ4CUnYCeHLhJmd14fQnWRcpiDT0AjqW3ISHEpBcZjYREaKuEOsSrIJNh7z2UxkLfTQ9MIAQFl8Bn1_WubyzVxvfKhs4HTJ2Z-0jdqMsapXq8kYUFpycTl3gYQJZ7NtSjISg-kk8zVcrB8z5x_5MMeOCdrhVClNyujofy9zjA5r1zEYVt_6BLWgOEUHOwMFu-hx-J6Fb4XPnoMJngEWwbiq814FzjsNJgu3j4XAbUCdggd-xoa_zCpSmdUZ-hi9TJ9ew5ogIdRxStYhcMItMaAJVToywlCFQehEakglFja2BLjwqUyildbcYKaE-0WtEpHB1pJz1CnmBVygADMrsKYSnAdA3dMUN9qJx4lKE8Nt2kODLWa5rqeHexKLr7zcRUQidyjnHuW8RrmH7huJRTU544-1XQ9ws67G9vL321do3wv7yC5OrlFnvdzADdrT3-vP1fK2VIsfh4K1FQ
linkProvider	IEEE
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1bS8MwFD7MC6gP3qZ4tw--CHZrmqRNHnwQL2yoY-CEvZUmOQFBurFNf79J2409iOBLaUsSwtdTzsm5fQBXeSryBPMkNJL5khxOwlwyEnLL80hRd4lVSTaR9npiOJT9BtwsamEQsUw-w5a_LWP5ZqS_vKus7WTJ6Z9kBdY4YzGpqrUWMQPGSjYuZzDQkIt0OA9KRrI9eOv7LK60FafOQvKOjiUltMSqUiqVp53_bWcXtmvjMbirvvYeNLDYh62lloJNuL177YfdwsfP0QQPiOOgV2V6TwNnnwZvY3eSxcAdQZ2IB77Lhn_sV7Qy0wN4f3oc3HfCmiIh1HFCZyEKKiw1qClTOjLSMEVQap5rTHIibWwpCumDmVQrrYUhqZLuJ7VKRoZYSw9htRgVeAQBSa0kmuXobADmVlPCaDc95irhRtjkGNpzzDJd9w_3NBafWXmOiGTmUM48ylmN8jFcL2aMq94Zf4xteoAX42psT35_fQkbncHrS_bS7T2fwqZfyPt5CT-D1dnkC89hXX_PPqaTi1JEfgAgs7hc
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=AMP-Inspired+Deep+Networks+for+Sparse+Linear+Inverse+Problems&rft.jtitle=IEEE+transactions+on+signal+processing&rft.au=Borgerding%2C+Mark&rft.au=Schniter%2C+Philip&rft.au=Rangan%2C+Sundeep&rft.date=2017-08-15&rft.issn=1053-587X&rft.eissn=1941-0476&rft.volume=65&rft.issue=16&rft.spage=4293&rft.epage=4308&rft_id=info:doi/10.1109%2FTSP.2017.2708040&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TSP_2017_2708040
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1053-587X&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1053-587X&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1053-587X&client=summon