Accelerated noncartesian sense reconstruction using a majorize-minimize algorithm combining variable-splitting

Magnetic resonance imaging (MRI) provides great flexibility in the choice of k-space sampling trajectories. NonCartesian trajectories exhibit several advantages over Cartesian ones but are less amenable to FFT-based manipulation of k-space data. Thus, existing iterative reconstruction methods for nonCartesian trajectories require relatively more computation (interpolation/gridding in addition to FFTs) and can be slow, especially for (undersampled) parallel MRI. In this work, we focus on SENSE-based regularized image reconstruction for nonCartesian trajectories and propose a majorize-minimize approach where we first majorize the SENSE data-fidelity term with a quadratic form involving a symmetric positive definite circulant matrix. For the minimization step, we apply a suitable variable splitting (VS) strategy combined with the augmented Lagrangian framework and alternating minimization that together decouple the circulant matrix from coil sensitivities and the regularizer. The resulting iterative algorithm admits simple update steps, is amenable to FFT-based matrix inversions due in part to the circulant matrix in the majorizer and provides a natural framework for incorporating a two-step procedure for acceleration. Simulations indicate that the proposed algorithm converges faster than some state-of-the-art VSbased iterative image reconstruction methods for the same problem.