Preconditioned P-ULA for Joint Deconvolution-Segmentation of Ultrasound Images -- Extended Version

Abstract

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.

References in corpus (4)

• A Survey of Stochastic Simulation and Optimization Methods in Signal Processing
• A quasi-Newton proximal splitting method
• Joint Image Restoration and Segmentation using Gauss-Markov-Potts Prior Models and Variational Bayesian Computation: Technical Details
• MM Algorithms for Minimizing Nonsmoothly Penalized Objective Functions

Cited by in corpus (4)

• Proximal Langevin Algorithm: Rapid Convergence Under Isoperimetry
• Accelerating proximal Markov chain Monte Carlo by using an explicit stabilised method
• Black-box sampling for weakly smooth Langevin Monte Carlo using p-generalized Gaussian smoothing
• Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm