Simultaneous phase correction and SENSE reconstruction for navigated multi‐shot DWI with non‐cartesian k‐space sampling

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Phase-navigated multi-shot acquisition and parallel imaging are two techniques that have been applied to diffusion-weighted imaging (DWI) to diminish distortions and to enhance spatial resolution. Specifically, sensitivity encoding (SENSE) has been combined with single-shot echo planar imaging (EPI). Thus far, it has been difficult to apply parallel imaging methods, like SENSE, to multi-shot DWI because motion-induced phase error varies from shot to shot and interferes with sensitivity encoding. Although direct phase subtraction methods have been introduced to correct this phase error, they generally are not suitable for SENSE reconstruction, and they cannot remove all the motion artifacts even if the phase error is fully known. Here, an effective algorithm is proposed to correct the motion-induced phase error using an iterative reconstruction. In this proposed conjugate-gradient (CG) algorithm, the phase error is treated as an image encoding function. Given the complex perturbation terms, diffusion-weighted images can be reconstructed using an augmented sensitivity map. The mathematical formulation and image reconstruction procedures of this algorithm are similar to the SENSE reconstruction. By defining a dynamic composite sensitivity, the CG phase correction method can be conveniently incorporated with SENSE reconstruction for the application of multi-shot SENSE DWI. Effective phase correction and multi-shot SENSE DWI (R = 1 to 3) are demonstrated on both simulated and in vivo data acquired with PROPELLER and SNAILS.