Efficient motion-corrected image reconstruction for 3D cardiac MRI through stochastic optimisation

<i>Objective.</i>Motion-corrected image reconstruction (MCIR) allows for fast and efficient cardiac magnetic resonance imaging (MRI) acquisition with predictable scan times. Since data obtained in all phases of respiratory and cardiac motion can be exploited, the duration of the scan is not affected by changes in heart rate or irregular breathing patterns. Achieving high-quality reconstructions from MCIR data typically requires iterative optimisation algorithms with regularisation, where reconstruction time increases with the number of motion states. This is particularly relevant in cardiac MRI, where both cardiac and respiratory motion corrections are necessary to minimise motion artefacts.<i>Approach.</i>In this work, we present a stochastic optimisation approach for efficient MCIR of 3D cardiac MRI images using the stochastic primal dual hybrid gradient (SPDHG) algorithm.<i>Main results.</i>In phantom experiments with simulated motion, we demonstrate the improved convergence rates of SPDHG with respect to deterministic algorithms, while maintaining image quality. Convergence is improved both in terms of reconstruction times and computational effort. We validate the method's effectiveness on an<i>in vivo</i>3D whole-heart cardiac MR scan. The<i>in vivo</i>method demonstrates that the motion compensation method we use allows for non-rigid deformations and irregular breathing patterns.<i>Significance.</i>This study demonstrates that stochastic algorithms can converge significantly faster than deterministic algorithms for MCIR, especially for a large number of motion states. With the proposed approach, increasing the number of motion states reduces the number of epochs required to reconstruct the image and therefore it is no longer necessary to balance the competing requirements of accurate motion correction and computational effort.