This work concerns estimation of optimal MRI images from incomplete raw data. 'Raw' implies that the data have not yet been Fourier transformed to the spatial (image) domain, whereas 'incomplete' pertains to the fact that a number of points on the Cartesian sampling grid were omitted in order to reduce the scan time. We introduce a novel SVD-based method for estimating the omitted samples, with the specificity of more accurate model design. This is achieved iteratively using a new multichannel configuration which enables the exploitation of existing correlation in the different channels. At the same time, care is taken to select grid points that carry maximum information. The positions of these points are such that estimation of omitted samples amounts to interpolation rather than extrapolation.
Dologlou, I., Van Ormondt, D., & Carayannis, G. (1996). MRI scan time reduction through non-uniform sampling and SVD-based estimation. Signal Processing, 55(2), 207–219. https://doi.org/10.1016/S0165-1684(96)00131-4