Compressed LISTA exploiting toeplitz structure

Rong Fu, Tianyao Huang, Yimin Liu, Yonina C. Eldar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Iterative Shrinkage Thresholding Algorithm (ISTA) has been widely applied to solve linear inverse problems. To increase the rate of convergence, Learned-ISTA (LISTA) adopts deep learning techniques to learn the optimal algorithm parameters like the mutual inhibition matrices and filter matrices, which significantly reduces the number of iterations. However, the size of the learned mutual inhibition matrix exhibits quadratic growth in the length of sparse signal, which restricts the applicability of LISTA in some large-scale problems. In many applications such as direction-of-arrival (DOA) estimation, the learned mutual inhibition matrix naturally has a Toeplitz structure. Here we exploit the Toeplitz structure and propose a convolutional network, namely LISTA-Toeplitz, to reduce the memory cost. Simulation results show that LISTA-Toeplitz outperforms traditional ISTA in convergence speed and achieves a level of accuracy comparable to LISTA in DOA simulation.

Original languageEnglish
Title of host publication2019 IEEE Radar Conference, RadarConf 2019
Number of pages6
ISBN (Electronic)9781728116792
StatePublished - Apr 2019
Externally publishedYes
Event2019 IEEE Radar Conference, RadarConf 2019 - Boston, United States
Duration: 22 Apr 201926 Apr 2019

Publication series

Name2019 IEEE Radar Conference, RadarConf 2019


Conference2019 IEEE Radar Conference, RadarConf 2019
Country/TerritoryUnited States


  • Convolutional network
  • Iterative Shrinkage Thresholding Algorithm
  • Learned-ISTA
  • Linear Inverse Problem
  • Single-snapshot DOA estimation
  • Toeplitz matrix

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Signal Processing
  • Instrumentation


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