${K}$ -Space and Image-Space Combination for Motion-Induced Phase-Error Correction in Self-Navigated Multicoil Multishot DWI

Motion during diffusion encodings leads to different phase errors in different shots of multishot diffusion-weighted acquisitions. Phase error incoherence among shots results in undesired signal cancellation when data from all shots are combined. Motion-induced phase error correction for multishot diffusion-weighted imaging (DWI) has been studied extensively and there exist multiple phase error correction algorithms. A commonly used correction method is the direct phase subtraction (DPS). DPS, however, can suffer from incomplete phase error correction due to the aliasing of the phase errors in the high spatial resolution phases. Furthermore, improper sampling density compensation is also a possible issue of DPS. Recently, motion-induced phase error correction was incorporated in the conjugate gradient (CG) image reconstruction procedure to get a nonlinear phase correction method that is also applicable to parallel DWI. Although the CG method overcomes the issues of DPS, its computational requirement is high. Further, CG restricts to sensitivity encoding (SENSE) for parallel reconstruction. In this paper, a new time-efficient and flexible
k
-space and image-space combination (KICT) algorithm for rigid body motion-induced phase error correction is introduced. KICT estimates the motion-induced phase errors in image space using the self-navigated capability of the variable density spiral trajectory. The correction is then performed in
k
-space. The algorithm is shown to overcome the problem of aliased phase errors. Further, the algorithm preserves the phase of the imaging object and receiver coils in the corrected
k
-space data, which is important for parallel imaging applications. After phase error correction, any parallel reconstruction method can be used. The KICT algorithm is tested with both simulated and in vivo data with both multishot single-coil and multishot multicoil acquisitions. We show that KICT correction results in diffusion-weighted images with higher signal-to-noise ratio (SNR) and fractional anisotropy (FA) maps with better resolved fiber tracts as compared to DPS. In peripheral-gated acquisitions, KICT is comparable to the CG method.