  Methods exploiting sparsity have been popular in imaging and signal
processing applications including compression, denoising, and imaging inverse
problems. Data-driven approaches such as dictionary learning and transform
learning enable one to discover complex image features from datasets and
provide promising performance over analytical models. Alternating minimization
algorithms have been particularly popular in dictionary or transform learning.
In this work, we study the properties of alternating minimization for
structured (unitary) sparsifying operator learning. While the algorithm
converges to the stationary points of the non-convex problem in general, we
prove rapid local linear convergence to the underlying generative model under
mild assumptions. Our experiments show that the unitary operator learning
algorithm is robust to initialization.
