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# Novel Algorithm for ℓ1 Wavelet-Based MR Image Reconstruction

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

### Joint Annual Meeting of the of the International Society for Magnetic Resonance in Medicine and the European Society for Magnetic Resonance in Medicine and Biology (ISMRM/ESMRMB '10), Stockholm, Sweden, May 1-7, 2010.

In fast MR imaging, reconstruction artifacts due to undersampled k-space can be greatly reduced by applying proper nonlinear reconstructions [1] based on image-sparsifying transforms. While state-of-the-art methods rely on total variation (TV), in this paper we propose to use wavelets instead, along with a very fast algorithm. Simulations and experimental results show our ability to reduce computational costs while maintaining SNR and image quality. We propose an iterative algorithm that also makes the technique computationally competitive. Our algorithm is versatile and can be used for any linear MR imaging problem, for instance SENSE [2].

References

1. M. Lustig, D. Donoho, J.M. Pauly, "Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging," Magnetic Resonance in Medicine, vol. 58, no. 6, pp. 1182-1195, December 2007.

2. K.P. Pruessmann, M. Weiger, M.B. Scheidegger, P. Boesiger, "SENSE: Sensitivity Encoding for Fast MRI," Magnetic Resonance in Medicine, vol. 42, no. 5, pp. 952-962, November 1999.

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