Application of Linear Prediction for Phase and Magnitude Correction in Partially Acquired MRI

Using the boxcar representation in the spatial domain and a signal-space representation of its frequency-weighted k-space, an iterative prediction method is developed to derive an improved low-resolution phase approximation for phase correction. Compared to the homodyne filter, the proposed predictor is found to be more efficient due to its capability of exhibiting an equivalent degree of performance using a lower number of fractional lines. The phase correction performance is illustrated using partially acquired susceptibility weighted images (SWI). An extension of the predictor into higher frequency regions of phase-encodes in conjunction with a signal-space projection in the frequency-weighted partial k-space is shown to provide restoration of fine structural details of sparse magnitude images. The application of subspace projection filtering is demonstrated using magnetic resonance angiogram (MRA).