Learning flipping and rotation invariant sparsifying transforms

Adaptive sparse representation has been heavily exploited in signal processing and computer vision. Recently, sparsifying transform learning received interest for its cheap computation and optimal updates in the alternating algorithms. In this work, we develop a methodology for learning a Flipping and Rotation Invariant Sparsifying Transform, dubbed FRIST, to better represent natural images that contain textures with various geometrical directions. The proposed alternating learning algorithm involves efficient optimal updates. We demonstrate empirical convergence behavior of the proposed learning algorithm. Preliminary experiments show the usefulness of FRIST for image sparse representation, segmentation, robust inpainting, and MRI reconstruction with promising performances.