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 real-time 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.