Reconstruction after rotational motion

Patient rotational motion during a scan causes the k-space sampling to be both irregular and undersampled. Conventional regridding requires an estimate of the sampling density at each measured point and is not strictly consistent with sampling theory. Here, a 2D problem is converted to a series of 1D regriddings by exact interpolation along the measured readouts. Each 1D regridding, expressed in matrix form, requires a matrix inversion to gain an exact solution. Undersampled regions make the matrix ill-conditioned but summing the matrix columns (without inversion) indicates the undersampled regions. The missing data could be reacquired, but in this study it is estimated using a Delaunay triangle-based linear interpolation on the original 2D data. The matrix conditioning is improved, leading to images with reduced artifacts compared to other regridding schemes. Furthermore, there is no requirement to estimate a density compensation function at each of the measured points.