A Robust Dictionary Learning Algorithm for Image Denoising

In many image processing applications, we encounter the problem of suppressing noise that obeys a non-Gaussian statistics. It is well known in the signal processing community that, in case of heavy-tailed non-Gaussian noise corruption, $\ell_1$ distortion is a more suitable metric for data fidelity. Dictionary based image denoising algorithms existing in the literature are typically aimed at minimizing the $\ell_2$ distortion metric, and hence not suitable for suppressing non-Gaussian or impulsive noise. In this paper, we develop a dictionary learning algorithm by minimizing the $\ell_1$ error. The proposed algorithm exploits the idea of iterative minimization of suitably weighted $\ell_2$ error. We refer to this algorithm as robust dictionary learning (RDL). We demonstrate that the proposed algorithm results in higher atom detection rate compared to the state-of-the-art $K$-SVD algorithm, both in case of Gaussian and non-Gaussian noise contamination. For real images, we observe clear superiority of the proposed RDL algorithm over its $\ell_2$ based counterpart, namely the $K$-SVD algorithm, in terms of the quality of denoised output.