Structured outlier models for robust dictionary learning

Robust dictionary learning algorithms seek to learn a dictionary while being robust to the presence of outliers in the training set. Often, the elements of the training set have an underlying structure due to, for example, their spatial relation or their similarity. When outliers are present as elements of the training set, they often inherit the underlying structure of the training set. This work capitalizes on such structure, encoded as an undirected graph connecting elements of the training set, and on sparsity-aware outlier modeling tools to develop robust dictionary learning algorithms. Not only do these algorithms yield a robust dictionary, but they also identify the outliers in the training set. Computationally efficient algorithms based on block coordinate descent and proximal gradient methods are developed.