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

## TL;DR

This paper introduces a novel accelerated Bayesian method using preconditioned P-ULA for joint deconvolution and segmentation of ultrasound images, significantly improving speed and quality over existing techniques.

## Contribution

It proposes a new hierarchical Bayesian framework with a preconditioned P-ULA scheme and a majorization-minimization approach for faster, high-quality ultrasound image processing.

## Key findings

- Achieves up to six times faster convergence than previous HMC methods.
- Provides high-quality deconvolution and segmentation results on simulated and real ultrasound data.
- Demonstrates robustness and efficiency in medical imaging applications.

## 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.