  Features based on sparse representation, especially using the synthesis
dictionary model, have been heavily exploited in signal processing and computer
vision. However, synthesis dictionary learning typically involves NP-hard
sparse coding and expensive learning steps. Recently, sparsifying transform
learning received interest for its cheap computation and its optimal updates in
the alternating algorithms. In this work, we develop a methodology for learning
Flipping and Rotation Invariant Sparsifying Transforms, dubbed FRIST, to better
represent natural images that contain textures with various geometrical
directions. The proposed alternating FRIST learning algorithm involves
efficient optimal updates. We provide a convergence guarantee, and demonstrate
the empirical convergence behavior of the proposed FRIST learning approach.
Preliminary experiments show the promising performance of FRIST learning for
sparse image representation, segmentation, denoising, robust inpainting, and
compressed sensing-based magnetic resonance image reconstruction.
