Supervised Dictionary Learning for Signals from Union of Subspaces

Dictionary learning algorithms are used to train an overcomplete dictionary from a set of signal examples such that the learnt dictionary provides sparse representations for a class of signals from which the training examples are sampled. In this work, we consider a specific class of signals, i.e., signals which belong to a union of subspaces, and we propose a dictionary learning algorithm for such type of signals by extending the popular K-SVD algorithm. Apart from the traditional sparsity model, we also incorporate the union of subspaces model into the dictionary learning algorithm. Various experiments using synthetic and real data demonstrate that the proposed algorithm recovers a dictionary which is closer to the underlying unknown dictionary than the one obtained from a simple K-SVD algorithm which do not make use of the additional structure contained in the signal examples.