PCLR: Phase-constrained low-rank model for compressive diffusion-weighted MRI

Abstract

Purpose: This work develops a compressive sensing approach for diffusion-weighted (DW) MRI. Theory and Methods: A phase-constrained low-rank (PCLR) approach was developed using the image coherence across the DW directions for efficient compressive DW MRI, while accounting for drastic phase changes across the DW directions, possibly as a result of eddy current, and rigid and nonrigid motions. In PCLR, a low-resolution phase estimation was used for removing phase inconsistency between DW directions. In our implementation, GRAPPA (generalized autocalibrating partial parallel acquisition) was incorporated for better phase estimation while allowing higher undersampling factor. An efficient and easy-to-implement image reconstruction algorithm, consisting mainly of partial Fourier update and singular value decomposition, was developed for solving PCLR. Results: The error measures based on diffusion-tensorderived metrics and tractography indicated that PCLR, with its joint reconstruction of all DW images using the image coherence, outperformed the frame-independent reconstruction through zero-padding FFT. Furthermore, using GRAPPA for phase estimation, PCLR readily achieved a four-fold undersampling. Conclusion: The PCLR is developed and demonstrated for compressive DW MRI. A four-fold reduction in k-space sampling could be readily achieved without substantial degradation of reconstructed images and diffusion tensor measures, making it possible to significantly reduce the data acquisition in DW MRI and/or improve spatial and angular resolutions.