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Phaseless super-resolution MRI: improvements based
on optical analogy
F. Hennel, R. Tian, M. Engel, K.P. Pruessmann
Institute for Biomedical Engineering, University of Zurich and ETH
Zurich, Zurich/SWITZERLAND
Purpose/Introduction: The method of super-resolution (SR) MRI
based on microscopic tagging (1) can be regarded as an analogue of
the harmonic excitation (or structured illumination) used in SR optics
(2, 3) to surpass the diffraction limit by shifting the normally inac-
cessible spatial frequencies into the aperture of the imaging system.
The phaseless character of the tag-based encoding (4) makes this
method a promising tool for MRI applications where the signal phase
is instable, e.g., diffusion tensor imaging. We explore this optical
analogy to improve the reconstruction of phaseless SR-MRI by a
suppression of Gibbs ringing and a correction of tagging distortions.
Subjects and Methods: A single-shot imaging sequence such as EPI
is preceded by a tagging module consisting of two RF pulses sepa-
rated by a gradient pulse of integral Dk. Low resolution single shot
images are reconstructed using a k-space window W(k) to limit the
Gibbs ringing, and transformed back to k-space following the mag-
nitude calculation to remove the random phase. The contributions
from the k-space bands shifted by ±Dk, introduced by the tagging, are
separated from the central band based on a phase cycle of the RF
pulses, shifted to their proper positions, Fourier transformed, phase-
corrected and summed up.
Results: The result is equal to the FT of the true k-space data mul-
tiplied by three shifted copies of the low-resolution k-space window:
Sfinal(k) = Strue(k) 9 [W(k + Dk) + W(k) + W(k - Dk)].
The resolution gain is thus maximally threefold when W is rectangular
and Dk is set to its width. This, however, leaves Gibbs ringing on the
low-resolution images, which propagates to the final SR image.
Results are better with a sine-trapezoidal window and the three bands
properly overlapping to produce a flat top of the final filter (Fig. 1).
The trade-off is a slightly reduced resolution gain.
Phaseless-encoded low resolution images (left) and SR images
reconstructed from them (middle) using different band overlapping
factors and filters (right).
Discussion/Conclusion: The k-space analysis of the tagging-based
phaseless super-resolution encoding, inspired by the methodology of structured illumination optics, reveals the maximum resolution gain
of this technique and enables a compromise between the resolution
gain and the strength of the anti-ringing filter. It also allows a cor-
rection of tag distortions caused by an inhomogeneous magnetic field.
EPI images of a resolution attainable only by multi-shot methods
could be obtained without the phase sensitivity characteristic to multi-
shot EPI (Fig. 2). Low resolution EPI (sum of all phaseless-encoded images, left) and a
SR image reconstructed from these (right).
