3Parallel magnetic resonance imaging with adaptive radius in k‐space (PARS): Constrained image reconstruction using k‐space locality in radiofrequency coil encoded data

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Abstract
A parallel image reconstruction algorithm is presented that exploits the k‐space locality in radiofrequency (RF) coil encoded data. In RF coil encoding, information relevant to reconstructing an omitted datum rapidly diminishes as a function of k‐space separation between the omitted datum and the acquired signal data. The proposed method, parallel magnetic resonance imaging with adaptive radius in k‐space (PARS), harnesses this physical property of RF coil encoding via a sliding‐kernel approach. Unlike generalized parallel imaging approaches that might typically involve inverting a prohibitively large matrix for arbitrary sampling trajectories, the PARS sliding‐kernel approach creates manageable and distributable independent matrices to be inverted, achieving both computational efficiency and numerical stability. An empirical method designed to measure total error power is described, and the total error power of PARS reconstructions is studied over a range of k‐space radii and accelerations, revealing “minimal‐error” conditions at comparatively modest k‐space radii. PARS reconstructions of undersampled in vivo Cartesian and non‐Cartesian data sets are shown and are compared selectively with traditional SENSE reconstructions. Various characteristics of the PARS k‐space locality constraint (such as the tradeoff between signal‐to‐noise ratio and artifact power and the relationship with iterative parallel conjugate gradient approaches or nonparallel gridding approaches) are discussed. Magn Reson Med 53:1383–1392, 2005.

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