x‐f choice: Reconstruction of undersampled dynamic MRI by data‐driven alias rejection applied to contrast‐enhanced angiography

Abstract

A technique for reconstructing dynamic undersampled MRI data, termed "x-f choice," was developed and applied to dynamic contrast-enhanced MR angiography (DCE-MRA). Regular undersampling in k-t space (a hybrid of k-space and time) creates aliasing in the conjugate x-f space that must be resolved. When regions in the object containing fast dynamic change are sparse, as in DCE-MRA, signal overlap caused by aliasing is often much less than the undersample factor would imply. x-f Choice reconstruction identifies overlapping signals using a model of the full non-aliased x-f space that is automatically generated from the undersampled data, and applies parallel imaging (PI) to separate them. No extra reference scans are required to generate either the model or the coil sensitivity maps. At each location in the reconstructed images, g-factor noise amplification is compared with predicted reconstruction errors to obtain an optimized solution. Acceleration factors greater than the number of receiver coils are possible, but are limited by the sparseness of the dynamic content and the signal-to-noise ratio (SNR) (in DCE-MRA the latter is dominant). Temporal fidelity was validated for up to a factor 10 speed-up using retrospectively undersampled data from a six-coil array. The method was tested on volunteers using fivefold prospective undersampling. Magn Reson Med 56:811-823, 2006.

Sparse Reconstruction Techniques in Magnetic Resonance Imaging

“…k-t SENSE is a form of k-t BLAST in which parallel imaging is incorporated to help resolve aliased pixels, enabling higher acceleration factors to be employed. Other k-t variants exist, including those that involve parallel imaging in a different way or use sparsifying transforms other than the temporal Fourier transform 52–54 .…”

Optimal sampling for “Noquist” reduced‐data cine magnetic resonance imaging

“…1,2,4,13,15,16 Nonuniform sampling was proposed by SPACE-RIP, 3 and was further investigated for SNR optimization in Ref. 17.…”

“…The Noquist method 7 preserves spatiotemporal resolution by a direct inversion approach, in contrast with techniques that use interpolation or spatiotemporal correlations to recover missing data. [8][9][10][11][12][13][14][15] With Noquist, a more sparsely sampled dynamic image sequence is reconstructed correctly without Nyquist foldover artifact by reductions in the size of the discrete Fourier model of the k-space data for the dynamic image. This allows imaging, compared to conventional imaging techniques, with a reduced imaging time at the same resolution.…”

Dictionary Learning and Time Sparsity for Dynamic MR Data Reconstruction

“…These look very different from the initial structured DCT dictionary. Some show coarse edges in different directions (atoms 5, 7, 8) whereas others do not have a significant structure and are necessary to capture image details (4,10,12). Furthermore, some contain temporal dynamism (1,3,20) while others are relatively static (5,8,11).…”

“…Methods like k-t BLAST [11] use a priori knowledge on the x-f support of the data obtained from a training process to prune a reconstruction that optimally reduces aliasing. Others like x-f choice [12] can learn the support region directly from the undersampled data.…”