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UID:20260923T011229EDT-7051W12hp2@132.216.98.100
DTSTAMP:20260923T051229Z
DESCRIPTION:Title : On compressed sensing with generative neural networks a
 nd Fourier measurements\n\nAbstract: In work by Bora et al. (2017)\, a mat
 hematical framework was developed for compressed sensing guarantees when t
 he measurement matrix is Gaussian and the signal structure is the range of
  a Lipschitz function (with applications to generative neural networks (GN
 Ns)). We consider measurement matrices derived by sampling uniformly at ra
 ndom rows of a unitary matrix (including subsampled Fourier measurements a
 s a special case). We prove the first known restricted isometry guarantee 
 for compressed sensing with GNNs and subsampled isometries\, and provide r
 ecovery bounds. Recovery efficacy is characterized by the coherence\, a ne
 w parameter\, which measures the interplay between the range of the networ
 k and the measurement matrix. Furthermore\, we propose a regularization st
 rategy for training GNNs to have favourable coherence with the measurement
  operator. We provide compelling numerical simulations that support this r
 egularized training strategy: our strategy yields low coherence networks t
 hat require fewer measurements for signal recovery. This\, together with o
 ur theoretical results\, supports coherence as a natural quantity for char
 acterizing generative compressed sensing with subsampled isometries.\n\nZo
 om Meeting :\n\nhttps://us06web.zoom.us/j/85327310903?pwd=SlhEak53S2xrNkVY
 Kzl4YUd5KzBudz09\n\nMeeting ID: 853 2731 0903\n\nPassword: 383854\n
DTSTART:20230123T213000Z
DTEND:20230123T223000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Aaron Berk (McGll University)
URL:https://www.mcgill.ca/mathstat/channels/event/aaron-berk-mcgll-universi
 ty-345048
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