Outlier-aware dictionary learning for sparse representation

Dictionary learning (DL) for sparse representation has been widely investigated during the last decade. A DL algorithm uses a training data set to learn a set of basis functions over which all training signals can be sparsely represented. In practice, training signals may contain a few outlier data, whose structures differ from those of the clean training set. The presence of these unpleasant data may heavily affect the learning performance of a DL algorithm. In this paper we propose a robust-to-outlier formulation of the DL problem. We then present an algorithm for solving the resulting problem. Experimental results on both synthetic data and image denoising demonstrate the promising robustness of our proposed problem.