  Over the years, computational imaging with accurate nonlinear physical models
has drawn considerable interest due to its ability to achieve high-quality
reconstructions. However, such nonlinear models are computationally demanding.
A popular choice for solving the corresponding inverse problems is accelerated
stochastic proximal methods (ASPMs), with the caveat that each iteration is
expensive. To overcome this issue, we propose a mini-batch quasi-Newton
proximal method (BQNPM) tailored to image-reconstruction problems with
total-variation regularization. It involves an efficient approach that computes
a weighted proximal mapping at a cost similar to that of the proximal mapping
in ASPMs. However, BQNPM requires fewer iterations than ASPMs to converge. We
assess the performance of BQNPM on three-dimensional inverse-scattering
problems with linear and nonlinear physical models. Our results on simulated
and real data show the effectiveness and efficiency of BQNPM,
