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Accelerated Convergent Motion Compensated Image Reconstruction

Claire Delplancke, Kris Thielemans, Matthias J. Ehrhardt

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.

Accelerated Convergent Motion Compensated Image Reconstruction

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.

Paper Structure

This paper contains 6 sections, 1 theorem, 3 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Method
  3. Model and algorithm
  4. Rates of convergence
  5. Numerical experiments
  6. Conclusions

Key Result

Theorem 1

For $N$ gates and well-chosen step-sizes $(\sigma_i),\tau,\theta$, the condition number and per-epoch convergence rate of SPDHG and PDHG are

Figures (3)

  • Figure 1: SPDHG's linear convergence is faster than PDHG's
  • Figure 2: Rigid motion
  • Figure 3: Non-rigid motion

Theorems & Definitions (1)

  • Theorem 1