A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance Imaging

Matthieu Guerquin-Kern (1) , Maximilian Häberlin (2) , Klaas P. Pruessmann (2) , Michael Unser (1)

1 Biomedical Imaging Group [Lausanne]
2 IBT - Institute for Biomedical Engineering [ETH Zürich]

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. Index Terms—Compressed sensing, fast iterative shrinkage/ thresholding algorithm (FISTA), fast weighted iterative shrinkage/ thresholding algorithm (FWISTA), iterative shrinkage/thresh-olding algorithm (ISTA), magnetic resonance imaging (MRI), non-Cartesian, nonlinear reconstruction, sparsity, thresholded Landweber, total variation, undersampled spiral, wavelets.

Mots clés: pressed sensing; iterative shrinkage/thresholding algorithm; ISTA; FISTA; FWISTA; thresholded Landweber; spiral; undersampled; nonlinear reconstruction; MRI; non-Cartesian; sparsity; wavelets; total variation; com-

Domaines: Traitement du signal et de l'image [eess.SP]; Imagerie médicale

Matthieu Guerquin-Kern, Maximilian Häberlin, Klaas P. Pruessmann, Michael Unser. A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance Imaging. IEEE Transactions on Medical Imaging, 2011, 30 (9), pp.1649-1660. ⟨10.1109/TMI.2011.2140121⟩. ⟨hal-01813870⟩