Combined higher order non-convex total variation with overlapping group sparsity for impulse noise removal

Tarmizi Adam, Raveendran Paramesran, Yin Mingming, Kuru Ratnavelu

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)


A typical approach to eliminate impulse noise is to use the ℓ1-norm for both the data fidelity term and the regularization terms. However, the ℓ1-norm tends to over penalize signal entries which is one of its underpinnings. Hence, we propose a variational model that uses the non-convex ℓp-norm, 0 < p < 1 for both the data fidelity and a second-order total variation regularization term combined with an overlapping group sparse regularizer. Specifically, to robustly eliminate impulse noise, the proposed method uses a non-convex data fidelity term. The hybrid combination of a second-order non-convex total variation and an overlapping group sparse regularization term is used to eliminate the remaining staircase artifacts while maintaining a sharp restored image. A mathematical formulation is derived and to implement it, the iterative re-weighted ℓ1 (IRL1) based alternating direction method of multipliers (ADMM) is used to solve the constraints and the subproblems. Experimental results for image denoising and deblurring on several widely used standard images demonstrate that the proposed method performed better when compared to the ℓ1-norm total variation (TV), total generalized variation (TGV) model, and the non-convex ℓp-norm TV-based data fidelity model in terms of peak signal-to-noise ratio (PSNR) and structure similarity index measure (SSIM).

Original languageEnglish
Pages (from-to)18503-18530
Number of pages28
JournalMultimedia Tools and Applications
Issue number12
Publication statusPublished - May 2021
Externally publishedYes


  • ADMM
  • Image restoration
  • Non-convex
  • Overlapping group sparsity
  • Total variation

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