Accelerated Convergent Motion Compensated Image Reconstruction

TL;DR

This paper introduces a randomized, convergent algorithm for motion compensated image reconstruction that significantly reduces computational costs, enabling faster processing of gated data with multiple motion states.

Contribution

The paper presents a novel randomized algorithm that maintains convergence while keeping per iteration costs constant regardless of the number of motion gates.

Findings

Improved theoretical convergence rates.

Observed speed-up on synthetic datasets.

Constant per iteration computational cost with multiple gates.

Abstract

Motion correction aims to prevent motion artefacts which may be caused by respiration, heartbeat, or head movements for example. In a preliminary step, the measured data is divided in gates corresponding to motion states, and displacement maps from a reference state to each motion state are estimated. One common technique to perform motion correction is the motion compensated image reconstruction framework, where the displacement maps are integrated into the forward model corresponding to gated data. For standard algorithms, the computational cost per iteration increases linearly with the number of gates. In order to accelerate the reconstruction, we propose the use of a randomized and convergent algorithm whose per iteration computational cost scales constantly with the number of gates. We show improvement on theoretical rates of convergence and observe the predicted speed-up on two synthetic datasets corresponding to rigid and non-rigid motion.