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

Objective 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. 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. Approach In this work, we present a stochastic optimisation approach for cardio-respiratory MCIR using the Stochastic Primal Dual Hybrid Gradient (SPDHG) algorithm. We compare the convergence rates with deterministic optimisation methods. Main Results 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 in vivo 3D whole-heart cardiac MR scan. The in vivo method demonstrates that the motion compensation method we use allows for non-rigid deformation patterns and irregular breathing patterns. Significance 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.