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.