  Sparsity-based models and techniques have been exploited in many signal
processing and imaging applications. Data-driven methods based on dictionary
and sparsifying transform learning enable learning rich image features from
data, and can outperform analytical models. In particular, alternating
optimization algorithms have been popular for learning such models. In this
work, we focus on alternating minimization for a specific structured unitary
sparsifying operator learning problem, and provide a convergence analysis.
While the algorithm converges to the critical points of the problem generally,
our analysis establishes under mild assumptions, the local linear convergence
of the algorithm to the underlying sparsifying model of the data. Analysis and
numerical simulations show that our assumptions hold for standard probabilistic
data models. In practice, the algorithm is robust to initialization.
