Fast Iterative Algorithm for the Reconstruction of Multishot Non-Cartesian Diffusion Data

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Purpose:To accelerate the motion-compensated iterative reconstruction of multishot non-Cartesian diffusion data.Method:The motion-compensated recovery of multishot non-Cartesian diffusion data is often performed using a modified iterative sensitivity-encoded algorithm. Specifically, the encoding matrix is replaced with a combination of nonuniform Fourier transforms and composite sensitivity functions, which account for the motion-induced phase errors. The main challenge with this scheme is the significantly increased computational complexity, which is directly related to the total number of composite sensitivity functions (number of shots × number of coils). The dimensionality of the composite sensitivity functions and hence the number of Fourier transforms within each iteration is reduced using a principal component analysis-based scheme. Using a Toeplitz-based conjugate gradient approach in combination with an augmented Lagrangian optimization scheme, a fast algorithm is proposed for the sparse recovery of diffusion data.Results:The proposed simplifications considerably reduce the computation time, especially in the recovery of diffusion data from under-sampled reconstructions using sparse optimization. By choosing appropriate number of basis functions to approximate the composite sensitivities, faster reconstruction (close to 9 times) with effective motion compensation is achieved.Conclusion:The proposed enhancements can offer fast motion-compensated reconstruction of multishot diffusion data for arbitrary k-space trajectories. Magn Reson Med 74:1086–1094, 2015. © 2014 Wiley Periodicals, Inc.

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