Dictionary learning based impulse noise removal via L1-L1 minimization

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-norm data-fidelity term to impulse noise cancellation. The restoration problem is mathematically formulated into an ℓ₁-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).