The recent global approach can learn convolutional operators without storing many overlapping patches. We propose 1) a new CAOL framework in the global approach, and 2) a new convergent Block Proximal Gradient method using Majorizer (BPG-M) to solve block multi-nonconvex problems. Numerical experiments show acceleration of CAOL via BPG-M and the effectiveness of tight-frame filters learned via CAOL for sparse-view CT reconstruction. Finally, we illustrate mathematical models for CNN via CAOL.

This presentation is part of Minisymposium “MS40 - Recent Advances in Convolutional Sparse Representations”
organized by: Giacomo Boracchi (Politecnico di Milano) , Alessandro Foi (Tampere University of Technology) , Brendt Wohlberg (Los Alamos National Laboratory) .

Authors:

Il Yong Chun (University of Michigan)

Jeffrey A. Fessler (University of Michigan)

Keywords:

block proximal gradient method using majorizer, computed tomography, convolutional neural network, convolutional operator learning, deep learning, image enhancement, image reconstruction, image representation, inverse problems, machine learning, nonlinear optimization