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

arXiv: https://arxiv.org/abs/1903.08111 · HTML: https://mlsanity.com/paper/1903.08111/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2019.

## Built on by (most cited first, 5 of 5)

- [Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2305.15988/) (2023)
- [Accelerated Bayesian imaging by relaxed proximal-point Langevin sampling](https://mlsanity.com/paper/2308.09460/) (2023)
- [Unadjusted Langevin algorithm for sampling a mixture of weakly smooth potentials](https://mlsanity.com/paper/2112.09311/) (2021)
- [A Variational Approach for Joint Image Recovery and Feature Extraction Based on Spatially-Varying Generalised Gaussian Models](https://mlsanity.com/paper/2209.01375/) (2022)
- [Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm](https://mlsanity.com/paper/2512.05791/) (2025)

## Abstract (arXiv)

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.