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Model-driven reconstruction with phase-constrained highly-oversampled MRI

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Document pages: 11 pages

Abstract: The Nyquist-Shannon theorem states that the information accessible bydiscrete Fourier protocols saturates when the sampling rate reaches twice thebandwidth of the detected continuous time signal. This maximum rate (theNS-limit) plays a prominent role in Magnetic Resonance Imaging (MRI).Nevertheless, reconstruction methods other than Fourier analysis can extractuseful information from data oversampled with respect to the NS-limit, giventhat relevant prior knowledge is available. Here we present PhasE-ConstrainedOverSampled MRI (PECOS), a method that exploits data oversampling incombination with prior knowledge of the physical interactions betweenelectromagnetic fields and spins in MRI systems. In PECOS, highlyoversampled-in-time k-space data are fed into a phase-constrained variant ofKaczmarz s algebraic reconstruction algorithm, where prior knowledge of theexpected spin contributions to the signal is codified into an encoding matrix.PECOS can be used for scan acceleration in relevant scenarios by oversamplingalong frequency-encoded directions, which is innocuous in MRI systems underreasonable conditions. We find situations in which the reconstruction qualitycan be higher than with NS-limited acquisitions and traditional Fourierreconstruction. Besides, we compare the performance of a variety of encodingpulse sequences as well as image reconstruction protocols, and find thataccelerated spiral trajectories in k-space combined with algebraicreconstruction techniques are particularly advantageous. The proposed samplingand reconstruction method is able to improve image quality for fully-sampledk-space trajectories, while allowing accelerated or undersampled acquisitionswithout regularization or signal extrapolation to unmeasured regions.

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