Robust Variants of Dictionary Learning Exploiting M-Estimators

We propose a robust alternative the well known dictionary learning technique K-SVD. Specifically, we exploit the theory behind M-Estimators to incorporate robustness into the sparse coding stage of K-SVD, and hence, decrease the estimation bias that might be introduced when outliers are present. Five different M-Estimators are introduced alongside their optimal hyperparameters in order to avoid parameter tuning by the user. In this way, the proposed framework has the same number of free parameters as K-SVD with the added feature of robustness and improved performance in non-Gaussian environments. We thoroughly demonstrate the superiority of the proposed algorithms via recovery of generating dictionaries for synthetic data and image denoising under two types of non-homogenous noise - salt and pepper noise, and impulsive noise.