Dictionary learning based impulse noise removal via L1–L1 minimization

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• Proposed the dictionary learning based impulse noise removal (DL-INR) algorithm.
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• Approached detail preservation by sparse representation over trained dictionary.
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• Formulated the dictionary learning task as an L1–L1 minimization problem.
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• Developed an augmented Lagrangian based solution to the L1–L1 minimization problem.
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• Both salt-and-pepper noise and random-valued noise are removed effectively.

To effectively remove impulse noise in natural images while keeping image details intact, this paper proposes a dictionary learning based impulse noise removal (DL-INR) algorithm, which explores both the strength of the patch-wise adaptive dictionary learning technique to image structure preservation and the robustness possessed by the ℓ1-normℓ1-norm data-fidelity term to impulse noise cancellation. The restoration problem is mathematically formulated into an ℓ1–ℓ1ℓ1–ℓ1 minimization objective and solved under the augmented Lagrangian framework through a two-level nested iterative procedure. We have compared the DL-INR algorithm to three median filter based methods, two state-of-the-art variational regularization based methods and a fixed dictionary based sparse representation method on restoring impulse noise corrupted natural images. The results suggest that DL-INR has a better ability to suppress impulse noise than other six algorithms and can produce restored images with higher peak signal-to-noise ratio (PSNR).