FRIST—flipping and rotation invariant sparsifying transform learning and applications. (21st June 2017)

• Record Type: Journal Article
• Authors: Wen, Bihan; Ravishankar, Saiprasad; Bresler, Yoram
• Is Part Of: Inverse problems. Volume 33:Number 7(2017:Jul.)
• Publication Date: 2017-06-21
• Subjects: sparsifying transform learning -- dictionary learning -- image denoising -- inpainting -- magnetic resonance imaging -- compressed sensing -- machine learning; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa6c6e
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.