Learning Sparsifying Transforms for Signal, Image, and Video Processing

The sparsity of signals and images in a certain transform domain or dictionary has been exploited in many applications in signal and image processing, including compression, denoising, and notably in compressed sensing, which enables accurate reconstruction from undersampled data. These various applications used sparsifying transforms such as DCT, wavelets, curvelets, and finite differences, all of which had a fixed, analytical data-independent form.

Recently, sparse representations that are directly adapted to the data have become popular, especially in applications such as image and video denoising and inpainting. While synthesis dictionary learning has enjoyed great popularity and analysis dictionary learning too has been explored, these methods involve a repeated step of sparse coding, which is NP hard, and heuristics for its approximation are computationally expensive. In this talk we describe our work on an alternative approach: sparsifying transform learning, in which a sparsifying transform is learned from data. The method provides efficient computational algorithms with exact closed-form solutions for the alternating optimization steps, and with theoretical convergence guarantees. The method scales better than dictionary learning with problem size and dimension, and in practice provides orders of magnitude speed improvements and better image quality in image processing applications. Variations on the method include the learning of a union of transforms, and online versions.

We describe applications to image representation, image and video denoising, and inverse problems in imaging, demonstrating improvements in performance and computation over state of the art methods.

Speaker: Yoram Bresler, Univ of Illinous at Urbana-Champaign