Online sparsifying transform learning for signal processing

Many techniques in signal and image processing exploit the sparsity of natural signals in a transform domain or dictionary. Adaptive synthesis dictionaries have been shown to be useful in applications such as signal denoising, and compressed sensing. More recently, the data-driven adaptation of sparsifying transforms has received some interest. The sparsifying transform model allows for exact and cheap computations. In this work, we propose a framework for online learning of square sparsifying transforms. Such online learning can be particularly useful when dealing with big data, and for signal processing applications such as realtime sparse representation and denoising. The proposed online transform learning algorithm is shown to have a much lower computational cost than online synthesis dictionary learning. The sequential learning of a sparsifying transform also typically converges faster than batch mode transform learning. Preliminary experiments show the usefulness of the proposed schemes for sparse representation, and denoising.