A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance Imaging

M. Guerquin-Kern, M. Häberlin, K.P. Pruessmann, M. Unser

IEEE Transactions on Medical Imaging, vol. 30, no. 9, pp. 1649-1660, September 2011.

In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space trajectories. Reconstruction is posed as an optimization problem that could be solved with the iterative shrinkage/thresholding algorithm (ISTA) which, unfortunately, converges slowly. To make the approach more practical, we propose a variant that combines recent improvements in convex optimization and that can be tuned to a given specific k-space trajectory. We present a mathematical analysis that explains the performance of the algorithms. Using simulated and in vivo data, we show that our nonlinear method is fast, as it accelerates ISTA by almost two orders of magnitude. We also show that it remains competitive with TV regularization in terms of image quality.

Erratum

• p. 1653, first column, Algorithm 3, update of v, the division bar is misplaced. The corrected equation should read v_n+1 ← w_n+1 + (t_n+1 − 1) (w_n+1 − w_n) ⁄ t_n;

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AUTHOR="Guerquin-Kern, M. and H{\"{a}}berlin, M. and Pruessmann, K.P.
        and Unser, M.",
TITLE="A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance
        Imaging",
JOURNAL="{IEEE} Transactions on Medical Imaging",
YEAR="2011",
volume="30",
number="9",
pages="1649--1660",
month="September",
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