A Conjugate-Gradient Approach to the Parameter Estimation Problem of Magnetic Resonance Advection Imaging

TL;DR

This paper introduces a conjugate-gradient method for estimating spatially varying pulse wave velocity in brain blood vessels from MRI data, improving upon previous techniques in accuracy and efficiency.

Contribution

The paper presents a novel conjugate-gradient algorithm tailored for the inverse problem in Magnetic Resonance Advection Imaging, addressing noisy operator challenges.

Findings

The proposed method outperforms existing algorithms in accuracy.

Numerical experiments demonstrate robustness to noise.

The approach is computationally efficient.

Abstract

We consider the inverse problem of estimating the spatially varying pulse wave velocity in blood vessels in the brain from dynamic MRI data, as it appears in the recently proposed imaging technique of Magnetic Resonance Advection Imaging (MRAI). The problem is formulated as a linear operator equation with a noisy operator and solved using a conjugate gradient type approach. Numerical examples on experimental data show the usefulness and advantages of the developed algorithm in comparison to previously proposed methods.