Dynamic Image and Fieldmap Joint Estimation Methods for MRI Using Single-Shot Trajectories
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Abstract: In susceptibility-weighted MRI, ignoring the magnetic field inhomogeneity can lead to severe reconstruction artifacts. Correcting for the effects of magnetic field inhomogeneity requires accurate fieldmaps. Especially in functional MRI, dynamic updates are desirable, since the fieldmap may change in time. Also, susceptibility effects that induce field inhomogeneity often have non-zero through-plane gradients, which, if uncorrected, can cause signal loss in the reconstructed images. Most image reconstruction methods that compensate for field inhomogeneity, even using dynamic fieldmap updates, ignore through-plane fieldmap gradients. Furthermore, standard optimization methods, like CG-based algorithms, may be slow to converge and recently proposed algorithms based on the Augmented Lagrangian (AL) framework have shown the potential to lead to more efficient optimization algorithms, especially in MRI reconstruction problems with non-quadratic regularization. In this work, we propose a computationally efficient, model-based iterative method for joint reconstruction of dynamic images and fieldmaps in single coil and parallel MRI, using single-shot trajectories. We first exploit the fieldmap smoothness to perform joint estimation using less than two full data sets and then we exploit the sensitivity encoding from parallel imaging to reduce the acquisition length and perform joint reconstruction using just one full k-space dataset. Subsequently, we extend the proposed method to account for the through-plane gradients of the field inhomogeneity. To improve the efficiency of the reconstruction algorithm we use a linearization technique for fieldmap estimation, which allows the use of the conjugate gradient algorithm. The resulting method allows for efficient reconstruction by applying fast approximations that allow the use of the conjugate gradient algorithm along with FFTs. Our proposed method can be computationally efficient for quadratic regularizers, but the CG-based algorithm is not directly applicable to non-quadratic regularization. To improve the efficiency of our method for non-quadratic regularization we propose an algorithm based on the augmented Lagrangian (AL) framework with variable splitting. This new algorithm can also be used for the non-linear optimization problem of fieldmap estimation without the need for the linearization approximation.