  Non-smooth regularization is widely used in image reconstruction to eliminate
the noise while preserving subtle image structures. In this work, we
investigate the use of proximal Newton (PN) method to solve an optimization
problem with a smooth data-fidelity term and total variation (TV)
regularization arising from image reconstruction applications. Specifically, we
consider a nonlinear Poisson-modeled single-energy X-ray computed tomography
reconstruction problem with the data-fidelity term given by the I-divergence.
The PN algorithm is compared to state-of-the-art first-order proximal
algorithms, such as the well-established fast iterative shrinkage and
thresholding algorithm (FISTA), both in terms of the number of iterations and
time to solutions. We discuss the key factors that influence the performance of
PN, including the strength of regularization, the stopping criterion for both
sub-problem and main-problem, and the use of exact or approximated Hessian
operators.
