Compressive manifold learning: estimating one-dimensional respiratory motion directly from undersampled k-space data.

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.