# Joint phase reconstruction and magnitude segmentation from velocity-encoded MRI data

## TL;DR

This paper introduces a joint optimization method using non-convex Bregman iteration to simultaneously estimate velocity, magnitude, and segmentation in velocity-encoded MRI, enhancing accuracy over traditional sequential methods.

## Contribution

The work presents a novel joint estimation algorithm for velocity, magnitude, and segmentation in velocity-encoded MRI data, improving upon classical approaches.

## Key findings

- Joint model outperforms sequential methods in accuracy
- Numerical experiments validate the approach on synthetic and real data
- Method effectively estimates dynamic flow components in bubbly flow imaging

## Abstract

Velocity-encoded MRI is an imaging technique used in different areas to assess flow motion. Some applications include medical imaging such as cardiovascular blood flow studies, and industrial settings in the areas of rheology, pipe flows, and reactor hydrodynamics, where the goal is to characterise dynamic components of some quantity of interest. The problem of estimating velocities from such measurements is a nonlinear dynamic inverse problem. To retrieve time-dependent velocity information, careful mathematical modelling and appropriate regularisation is required. In this work, we propose an optimisation algorithm based on non-convex Bregman iteration to jointly estimate velocity-, magnitude- and segmentation-information for the application of bubbly flow imaging. Furthermore, we demonstrate through numerical experiments on synthetic and real data that the joint model improves velocity, magnitude and segmentation over a classical sequential approach.