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Compressive manifold learning: Estimating one‐dimensional respiratory motion directly from undersampled k‐space data
Author(s) -
Usman Muhammad,
Vaillant Ghislain,
Atkinson David,
Schaeffter Tobias,
Prieto Claudia
Publication year - 2014
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.25010
Subject(s) - motion (physics) , nonlinear dimensionality reduction , manifold (fluid mechanics) , space (punctuation) , computer science , artificial intelligence , compressed sensing , computer vision , dimensionality reduction , mechanical engineering , engineering , operating system
Purpose To present and validate a manifold learning (ML)‐based method that estimates the respiratory signal directly from undersampled k‐space data and that can be applied for respiratory self‐gated liver MRI. Methods ML methods embed high‐dimensional space data in a low‐dimensional space while preserving their characteristic properties. These methods have been used to estimate one‐dimensional respiratory motion (low‐dimensional manifold) from a set of high‐dimensional free‐breathing abdominal MR images. These approaches require MR images to be reconstructed first from the acquired undersampled data. Recently, the concept of compressive manifold learning (CML) has been introduced that combines compressed sensing with ML by learning low‐dimensional manifolds directly from a partial set of compressed measurements, provided that the sampling satisfies the restricted isometry property. We propose to use the CML concept to extract the respiratory signal directly from undersampled k‐space data. Results Simulation results from free‐breathing abdominal MR data show that CML can accurately estimate respiratory motion from highly retrospectively undersampled k‐space (up to 25‐fold acceleration under ideal assumptions). Prospective free‐breathing golden‐angle radial two‐dimensional (2D) acquisitions further demonstrate the feasibility of the CML method for respiratory self‐gating acquisition, estimating the respiratory motion from up to 15‐fold accelerated MR data. Conclusion The proposed method performs accurate respiratory signal estimation from highly undersampled k‐space data and can be used for respiratory self‐navigated 2D liver MRI. Magn Reson Med 72:1130–1140, 2014. © 2013 Wiley Periodicals, Inc.