Statistically driven sparse image approximation

Rosa M. Figueras i Ventura, Eero Simoncelli

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Finding the sparsest approximation of an image as a sum of basis functions drawn from a redundant dictionary is an NP-hard problem. In the case of a dictionary whose elements form an overcomplete basis, a recently developed method, based on alternating thresholding and projection operations, provides an appealing approximate solution. When applied to images, this method produces sparser results and requires less computation than current alternative methods. Motivated by recent developments in statistical image modeling, we develop an enhancement of this method based on a locally adaptive threshold operation, and demonstrate that the enhanced algorithm is capable of finding sparser approximations with a decrease in computational complexity.

Original languageEnglish (US)
Title of host publication2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings
Volume1
DOIs
StatePublished - 2006
Event14th IEEE International Conference on Image Processing, ICIP 2007 - San Antonio, TX, United States
Duration: Sep 16 2007Sep 19 2007

Other

Other14th IEEE International Conference on Image Processing, ICIP 2007
CountryUnited States
CitySan Antonio, TX
Period9/16/079/19/07

Fingerprint

Glossaries
Computational complexity

Keywords

  • Image statistics
  • Overcomplete representation
  • Redundant dictionary
  • Sparse image approximation

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Figueras i Ventura, R. M., & Simoncelli, E. (2006). Statistically driven sparse image approximation. In 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings (Vol. 1). [4378991] https://doi.org/10.1109/ICIP.2007.4378991

Statistically driven sparse image approximation. / Figueras i Ventura, Rosa M.; Simoncelli, Eero.

2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings. Vol. 1 2006. 4378991.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Figueras i Ventura, RM & Simoncelli, E 2006, Statistically driven sparse image approximation. in 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings. vol. 1, 4378991, 14th IEEE International Conference on Image Processing, ICIP 2007, San Antonio, TX, United States, 9/16/07. https://doi.org/10.1109/ICIP.2007.4378991
Figueras i Ventura RM, Simoncelli E. Statistically driven sparse image approximation. In 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings. Vol. 1. 2006. 4378991 https://doi.org/10.1109/ICIP.2007.4378991
Figueras i Ventura, Rosa M. ; Simoncelli, Eero. / Statistically driven sparse image approximation. 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings. Vol. 1 2006.
@inproceedings{6f3c4ec63bfb4af398d91fc77bda8556,
title = "Statistically driven sparse image approximation",
abstract = "Finding the sparsest approximation of an image as a sum of basis functions drawn from a redundant dictionary is an NP-hard problem. In the case of a dictionary whose elements form an overcomplete basis, a recently developed method, based on alternating thresholding and projection operations, provides an appealing approximate solution. When applied to images, this method produces sparser results and requires less computation than current alternative methods. Motivated by recent developments in statistical image modeling, we develop an enhancement of this method based on a locally adaptive threshold operation, and demonstrate that the enhanced algorithm is capable of finding sparser approximations with a decrease in computational complexity.",
keywords = "Image statistics, Overcomplete representation, Redundant dictionary, Sparse image approximation",
author = "{Figueras i Ventura}, {Rosa M.} and Eero Simoncelli",
year = "2006",
doi = "10.1109/ICIP.2007.4378991",
language = "English (US)",
isbn = "1424414377",
volume = "1",
booktitle = "2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings",

}

TY - GEN

T1 - Statistically driven sparse image approximation

AU - Figueras i Ventura, Rosa M.

AU - Simoncelli, Eero

PY - 2006

Y1 - 2006

N2 - Finding the sparsest approximation of an image as a sum of basis functions drawn from a redundant dictionary is an NP-hard problem. In the case of a dictionary whose elements form an overcomplete basis, a recently developed method, based on alternating thresholding and projection operations, provides an appealing approximate solution. When applied to images, this method produces sparser results and requires less computation than current alternative methods. Motivated by recent developments in statistical image modeling, we develop an enhancement of this method based on a locally adaptive threshold operation, and demonstrate that the enhanced algorithm is capable of finding sparser approximations with a decrease in computational complexity.

AB - Finding the sparsest approximation of an image as a sum of basis functions drawn from a redundant dictionary is an NP-hard problem. In the case of a dictionary whose elements form an overcomplete basis, a recently developed method, based on alternating thresholding and projection operations, provides an appealing approximate solution. When applied to images, this method produces sparser results and requires less computation than current alternative methods. Motivated by recent developments in statistical image modeling, we develop an enhancement of this method based on a locally adaptive threshold operation, and demonstrate that the enhanced algorithm is capable of finding sparser approximations with a decrease in computational complexity.

KW - Image statistics

KW - Overcomplete representation

KW - Redundant dictionary

KW - Sparse image approximation

UR - http://www.scopus.com/inward/record.url?scp=48149107003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=48149107003&partnerID=8YFLogxK

U2 - 10.1109/ICIP.2007.4378991

DO - 10.1109/ICIP.2007.4378991

M3 - Conference contribution

AN - SCOPUS:48149107003

SN - 1424414377

SN - 9781424414376

VL - 1

BT - 2007 IEEE International Conference on Image Processing, ICIP 2007 Proceedings

ER -