RT Journal Article
T1 The noise collector for sparse recovery in high dimensions
A1 Moscoso, Miguel
A1 Novikov, Alexei
A1 Papanicolaou, George
A1 Tsogka, Chrysoula
AB The ability to detect sparse signals from noisy, high-dimensional data is a top priority in modern science and engineering. It is well known that a sparse solution of the linear system Alpharho=b0 can be found efficiently with an l1-norm minimization approach if the data  are  noiseless.  However,  detection  of  the  signal  from  data corrupted by noise is still a challenging problem as the solution depends,  in  general,  on  a  regularization  parameter  with  optimal  value  that  is  not  easy  to  choose.  We  propose  an  efficient approach  that  does  not  require  any  parameter  estimation.  We introduce a no-phantom weight tau and the Noise Collector matrix C and solve an augmented system Alpharho+Ceta=b0+e, where e is the  noise.  We  show  that  the l1-norm  minimal  solution  of  this system has zero false discovery rate for any level of noise, with probability  that  tends  to  one  as  the  dimension  of b0 increases to infinity. We obtain exact support recovery if the noise is not too  large  and  develop  a  fast  Noise  Collector  algorithm,  which makes  the  computational  cost  of  solving  the  augmented  system comparable with that of the original one. We demonstrate the effectiveness of the method in applications to passive array imaging.
PB National Academy of Sciences
SN 1091-6490
SN 0027-8424 (online)
YR 2020
FD 2020-05-26
LK https://hdl.handle.net/10016/32485
UL https://hdl.handle.net/10016/32485
LA eng
NO The work of M.M. was partially supported by Spanish Ministerio de Ciencia e Innovación Grant FIS2016-77892-R. The work of A.N. was partially supported by NSF Grants DMS-1515187 and DMS-1813943. The work of G.P. was partially supported by Air Force Office of Scientific Research (AFOSR) Grant FA9550-18-1-0519. The work of C.T. was partially supported by AFOSR Grants FA9550-17-1-0238 and FA9550-18-1-0519.
DS e-Archivo
RD 26 jun. 2024