Efficient and Robust Image Restoration Using Multiple-Feature L2-Relaxed Sparse Analysis Priors

Javier Portilla, Antonio Tristan-Vega, Ivan Selesnick

Research output: Contribution to journalArticle

Abstract

We propose a novel formulation for relaxed analysis-based sparsity in multiple dictionaries as a general type of prior for images, and apply it for Bayesian estimation in image restoration problems. Our formulation of a ℓ2-relaxed ℓ0 pseudo-norm prior allows for an especially simple maximum a posteriori estimation iterative marginal optimization algorithm, whose convergence we prove. We achieve a significant speedup over the direct (static) solution by using dynamically evolving parameters through the estimation loop. As an added heuristic twist, we fix in advance the number of iterations, and then empirically optimize the involved parameters according to two performance benchmarks. The resulting constrained dynamic method is not just fast and effective, it is also highly robust and flexible. First, it is able to provide an outstanding tradeoff between computational load and performance, in visual and objective, mean square error and structural similarity terms, for a large variety of degradation tests, using the same set of parameter values for all tests. Second, the performance benchmark can be easily adapted to specific types of degradation, image classes, and even performance criteria. Third, it allows for using simultaneously several dictionaries with complementary features. This unique combination makes ours a highly practical deconvolution method.

Original languageEnglish (US)
Article number7265041
Pages (from-to)5046-5059
Number of pages14
JournalIEEE Transactions on Image Processing
Volume24
Issue number12
DOIs
StatePublished - Dec 1 2015

Fingerprint

Image reconstruction
Glossaries
Degradation
Deconvolution
Mean square error

Keywords

  • fast constrained dynamic algorithm
  • Image restoration
  • L2-relaxed L0 pseudo norm
  • L2-relaxed sparse analysis priors
  • maximum a posteriori estimation
  • multiple representations
  • robust tunable parameters

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software

Cite this

Efficient and Robust Image Restoration Using Multiple-Feature L2-Relaxed Sparse Analysis Priors. / Portilla, Javier; Tristan-Vega, Antonio; Selesnick, Ivan.

In: IEEE Transactions on Image Processing, Vol. 24, No. 12, 7265041, 01.12.2015, p. 5046-5059.

Research output: Contribution to journalArticle

@article{419917a8bb1b42b7b7b84f17ffad8864,
title = "Efficient and Robust Image Restoration Using Multiple-Feature L2-Relaxed Sparse Analysis Priors",
abstract = "We propose a novel formulation for relaxed analysis-based sparsity in multiple dictionaries as a general type of prior for images, and apply it for Bayesian estimation in image restoration problems. Our formulation of a ℓ2-relaxed ℓ0 pseudo-norm prior allows for an especially simple maximum a posteriori estimation iterative marginal optimization algorithm, whose convergence we prove. We achieve a significant speedup over the direct (static) solution by using dynamically evolving parameters through the estimation loop. As an added heuristic twist, we fix in advance the number of iterations, and then empirically optimize the involved parameters according to two performance benchmarks. The resulting constrained dynamic method is not just fast and effective, it is also highly robust and flexible. First, it is able to provide an outstanding tradeoff between computational load and performance, in visual and objective, mean square error and structural similarity terms, for a large variety of degradation tests, using the same set of parameter values for all tests. Second, the performance benchmark can be easily adapted to specific types of degradation, image classes, and even performance criteria. Third, it allows for using simultaneously several dictionaries with complementary features. This unique combination makes ours a highly practical deconvolution method.",
keywords = "fast constrained dynamic algorithm, Image restoration, L2-relaxed L0 pseudo norm, L2-relaxed sparse analysis priors, maximum a posteriori estimation, multiple representations, robust tunable parameters",
author = "Javier Portilla and Antonio Tristan-Vega and Ivan Selesnick",
year = "2015",
month = "12",
day = "1",
doi = "10.1109/TIP.2015.2478405",
language = "English (US)",
volume = "24",
pages = "5046--5059",
journal = "IEEE Transactions on Image Processing",
issn = "1057-7149",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "12",

}

TY - JOUR

T1 - Efficient and Robust Image Restoration Using Multiple-Feature L2-Relaxed Sparse Analysis Priors

AU - Portilla, Javier

AU - Tristan-Vega, Antonio

AU - Selesnick, Ivan

PY - 2015/12/1

Y1 - 2015/12/1

N2 - We propose a novel formulation for relaxed analysis-based sparsity in multiple dictionaries as a general type of prior for images, and apply it for Bayesian estimation in image restoration problems. Our formulation of a ℓ2-relaxed ℓ0 pseudo-norm prior allows for an especially simple maximum a posteriori estimation iterative marginal optimization algorithm, whose convergence we prove. We achieve a significant speedup over the direct (static) solution by using dynamically evolving parameters through the estimation loop. As an added heuristic twist, we fix in advance the number of iterations, and then empirically optimize the involved parameters according to two performance benchmarks. The resulting constrained dynamic method is not just fast and effective, it is also highly robust and flexible. First, it is able to provide an outstanding tradeoff between computational load and performance, in visual and objective, mean square error and structural similarity terms, for a large variety of degradation tests, using the same set of parameter values for all tests. Second, the performance benchmark can be easily adapted to specific types of degradation, image classes, and even performance criteria. Third, it allows for using simultaneously several dictionaries with complementary features. This unique combination makes ours a highly practical deconvolution method.

AB - We propose a novel formulation for relaxed analysis-based sparsity in multiple dictionaries as a general type of prior for images, and apply it for Bayesian estimation in image restoration problems. Our formulation of a ℓ2-relaxed ℓ0 pseudo-norm prior allows for an especially simple maximum a posteriori estimation iterative marginal optimization algorithm, whose convergence we prove. We achieve a significant speedup over the direct (static) solution by using dynamically evolving parameters through the estimation loop. As an added heuristic twist, we fix in advance the number of iterations, and then empirically optimize the involved parameters according to two performance benchmarks. The resulting constrained dynamic method is not just fast and effective, it is also highly robust and flexible. First, it is able to provide an outstanding tradeoff between computational load and performance, in visual and objective, mean square error and structural similarity terms, for a large variety of degradation tests, using the same set of parameter values for all tests. Second, the performance benchmark can be easily adapted to specific types of degradation, image classes, and even performance criteria. Third, it allows for using simultaneously several dictionaries with complementary features. This unique combination makes ours a highly practical deconvolution method.

KW - fast constrained dynamic algorithm

KW - Image restoration

KW - L2-relaxed L0 pseudo norm

KW - L2-relaxed sparse analysis priors

KW - maximum a posteriori estimation

KW - multiple representations

KW - robust tunable parameters

UR - http://www.scopus.com/inward/record.url?scp=84959488985&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959488985&partnerID=8YFLogxK

U2 - 10.1109/TIP.2015.2478405

DO - 10.1109/TIP.2015.2478405

M3 - Article

AN - SCOPUS:84959488985

VL - 24

SP - 5046

EP - 5059

JO - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

SN - 1057-7149

IS - 12

M1 - 7265041

ER -