  Joint deconvolution and segmentation of ultrasound images is a challenging
problem in medical imaging. By adopting a hierarchical Bayesian model, we
propose an accelerated Markov chain Monte Carlo scheme where the tissue
reflectivity function is sampled thanks to a recently introduced proximal
unadjusted Langevin algorithm. This new approach is combined with a
forward-backward step and a preconditioning strategy to accelerate the
convergence, and with a method based on the majorization-minimization principle
to solve the inner nonconvex minimization problems. As demonstrated in
numerical experiments conducted on both simulated and in vivo ultrasound
images, the proposed method provides high-quality restoration and segmentation
results and is up to six times faster than an existing Hamiltonian Monte Carlo
method.
