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.