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

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Abstract

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).

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Notes

  1. Matlab codes can be downloaded at github.com/tarmiziAdam2005.

  2. The ℓ1-TV model has been presented in several papers for example in [49] and [9]. We use the ADMM/ALM formulation that closely follows the paper of [9].

  3. We used the ADMM implementation provided by the authors of [15]. However, we did not use the predictor-corrector approach.

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Authors and Affiliations

  1. Institute of Computer Science and Digital Innovation, UCSI University, 56000, Kuala Lumpur, Malaysia

    Tarmizi Adam, Raveendran Paramesran & Kuru Ratnavelu

  2. Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia

    Yin Mingming

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  1. Tarmizi Adam
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  2. Raveendran Paramesran
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  3. Yin Mingming
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  4. Kuru Ratnavelu
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Correspondence to Tarmizi Adam.

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Adam, T., Paramesran, R., Mingming, Y. et al. Combined higher order non-convex total variation with overlapping group sparsity for impulse noise removal. Multimed Tools Appl 80, 18503–18530 (2021). https://doi.org/10.1007/s11042-021-10583-y

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