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On Theoretical Limits in Parallel Magnetic Resonance Imaging

Frank Bauer, Christian Clason


Based on a Fourier series expression of true image, receiver sensitivities, and measurements, it is possible to give theoretical limits for the perfect reconstructability of image and sensitivities in parallel magnetic resonance imaging. These limits depend on the smoothness of the sensitivities, number of receiver coils, and size of the acquired k-space measurement window. Dierent types of a priori information can be incorporated in the determination of these limits. Numerical examples illustrate the theoretical results.


Magnetic resonance imaging, Image reconstruction, Fourier series, Newton method

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