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

Javier Portilla, Antonio Tristan-Vega, Ivan W. Selesnick

Research output: Contribution to journalArticlepeer-review


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
Issue number12
StatePublished - Dec 2015


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

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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