Deterministic Fourier-Based Dictionary Design for Sparse Reconstruction

D.D. Ariananda, H. Jamali-Rad, Zijian Tang, G. Leus, X. Campman

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

5 Citations (Scopus)

Abstract

This paper focuses on the design of a Fourier dictionary matrix formed by selecting specific rows of the inverse discrete Fourier transform matrix based on coherence-related metrics. While maximum coherence is a popular metric in compressive sampling, we also consider rms LN-coherence, which focuses on the largest LN (instead of one) inner products between different columns of the dictionary matrix. Finding a dictionary matrix optimizing either the maximum or the rms LN-coherence lead to a complicated optimization problem. Hence, we introduce a new metric called coherence deviation (CD), which gives a measure on the variation of all the inner products between different columns of the dictionary matrix, and motivate its use as an amenable alternative for both the maximum and rms LN-coherence. While finding a dictionary matrix optimizing the CD leads to a simplified optimization problem, the resulting cost function is a quartic function of a binary vector variable. Hence, we propose Greedy-β algorithm to provide sub-optimal solutions.
Original languageEnglish
Title of host publication2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)
Place of PublicationPiscataway, NJ
PublisherIEEE
Pages1-5
Number of pages5
ISBN (Electronic)978-1-5090-2103-1
DOIs
Publication statusPublished - 19 Sep 2016
Event2016 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM - Rio de Janeiro, Brazil
Duration: 10 Jul 201613 Jul 2016
Conference number: 9
https://www.ieee.org/conferences_events/conferences/conferencedetails/index.html?Conf_ID=35132
http://delamare.cetuc.puc-rio.br/sam2016/index.html

Conference

Conference2016 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM
Abbreviated titleSAM
CountryBrazil
CityRio de Janeiro
Period10/07/1613/07/16
Internet address

Keywords

  • Coherence
  • Dictionaries
  • Measurement
  • Discrete Fourier transforms
  • Indexes
  • Minimization
  • Sparse matrices

Fingerprint Dive into the research topics of 'Deterministic Fourier-Based Dictionary Design for Sparse Reconstruction'. Together they form a unique fingerprint.

Cite this