Higher dimensional homodyne filtering for suppression of incidental phase artifacts in multichannel MRI

The aim of this paper is to introduce procedural steps for extension of the 1D homodyne phase correction for k-space truncation in all gradient encoding directions. Compared to the existing method applied to 2D partial k-space, signal losses introduced by the phase correction filter is observed to be minimal for the extended approach. In addition, the modified form of phase correction mitigates Incidental Phase Artifacts (IPA) due to truncation. For parallel imaging with undersampling along phase encode direction, the extended homodyne filtering is shown to be effective for minimizing these artifacts when each of the channel k-spaces are truncated along both phase and frequency encode directions. This is illustrated with 2D partial k-space for flow compensated multichannel Susceptibility Weighted Imaging (SWI). Extension of our method to 3D partial k-space shows improved reconstruction of flow information in phase contrast angiography.

Least-Squares FIR Models of Low-Resolution MR data for Efficient Phase-Error Compensation with Simultaneous Artefact Removal

Signal space models in both phase-encode, and frequency-encode directions are presented for extrapolation of 2D partial kspace. Using the boxcar representation of low-resolution spatial data, and a geometrical representation of signal space vectors in both positive and negative phase-encode directions, a robust predictor is constructed using a series of signal space projections. Compared to some of the existing phase-correction methods that require acquisition of a pre-determined set of fractional kspace lines, the proposed predictor is found to be more efficient, due to its capability of exhibiting an equivalent degree of performance using only half the number of fractional lines. Robust filtering of noisy data is achieved using a second signal space model in the frequency-encode direction, bypassing the requirement of a prior highpass filtering operation. The signal space is constructed from Fourier Transformed samples of each row in the low-resolution image. A set of FIR filters are estimated by fitting a least squares model to this signal space. Partial kspace extrapolation using the FIR filters is shown to result in artifact-free reconstruction, particularly in respect of Gibbs ringing and streaking type artifacts.