A Compressed Sensing Framework for Magnetic Resonance Fingerprinting

Mike Davies just sent me the following:

Hi Igor

....

Given you enthusiasm for the recent "magnetic resonance fingerprinting" paper, may I also take this opportunity to let you know of some new work that I have done with Gilles Puy, Yves Wiaux and Pierre Vandergheynst. Specifically we have considered the problem from a rigorous CS perspective. This gave us insight on the requirements of the excitation sequence, how to sub-sample k-space and a provably good reconstruction algorithm - Bloch response recovery via Iterated Projection (BLIP), a variant on IHT based on work of Thomas Blumensath. Simulations show significant performance gains over the already good MRF scheme. The relevant articles can be found at http://arxiv.org/abs/1312.2465 and http://arxiv.org/abs/1312.2457 . Enjoy!

All the best

Mike

Thanks Mike ! I love this statement :

The procedure works through a form of noise averaging. Although each individual image is very noisy, the noise is greatly reduced when the voxel sequences are projected onto the Bloch response manifold. However, this ignores the main tenet of compressed sensing - aliasing is not noise but interference and under the right circumstances it can be completely removed. We explore this idea next.

I also love the open questions at the very end. Here are the preprints: A Compressed Sensing Framework for Magnetic Resonance Fingerprinting by Mike Davies, Gilles Puy, Pierre Vandergheynst, Yves Wiaux

Inspired by the recently proposed Magnetic Resonance Fingerprinting (MRF) technique we develop a principled compressed sensing framework for quantitative MRI. The three key components are: a random pulse excitation sequence following the MRF technique; a random EPI subsampling strategy and an iterative projection algorithm that imposes consistency with the Bloch equations. We show that, as long as the excitation sequence possesses an appropriate form of persistent excitation, we are able to achieve accurate recovery the proton density, T1, T2 and off-resonance maps simultaneously from a limited number of samples.

and Compressed Quantitative MRI: Bloch Response Recovery through Iterated Projection by Mike Davies, Gilles Puy, Pierre Vandergheynst, Yves Wiaux

Inspired by the recently proposed Magnetic Resonance Fingerprinting technique, we develop a principled compressed sensing framework for quantitative MRI. The three key components are: a random pulse excitation sequence following the MRF technique; a random EPI subsampling strategy and an iterative projection algorithm that imposes consistency with the Bloch equations. We show that, as long as the excitation sequence possesses an appropriate form of persistent excitation, we are able to achieve accurate recovery of the proton density, T1, T2 and off-resonance maps simultaneously from a limited number of samples.

Join the CompressiveSensing subreddit or the Google+ Community and post there !

Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.