Compressive manifold learning: Estimating 1D respiratory motion directly from undersampled k-space data

Abstract

ML methods embed high-dimensional space data in a low-dimensional space, while preserving their characteristics properties. These methods have been used to estimate 1D 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 data and therefore are not applicable for commonly used undersampled acquisitions. 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 ofcompressed 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 from free-breathing abdominal MR data show that CML can accurately estimate respiratory motion from highly retrospectively undersampled k-space (up to 25-foldacceleration). Prospective free-breathing golden angle radial 2D acquisitions further demonstrate the feasibility of the CML method for respiratory self-gating acquisition.The proposed method performs accurate respiratory signal estimation from highly undersampled k-space data and can be used for respiratory self-navigated 2D liver MR imaging.