ABSTRACT
Chapter 4 discusses the problems related to a single-filter calibration due to the SNR variation of the MR signal across different k-space locations. Methods developed with the goal of addressing these problems suggest modifications to the filter calibration using either some form of weighting applied to the regression model or estimation of parameters based on k-space location. The different types of multi-filter approaches include modeling non-stationarity of kernel weights (MONKEES), spatially variant (SV)-GRAPPA, and frequency-dependent regularization (FDR). MONKEES GRAPPA exploits the idea that k-space magnitudes decrease with increasing distance from the k-space centre to estimate separate GRAPPA weights for each cluster obtained by partitioning the k-space based on the average magnitude. Alternatively, SV-GRAPPA uses the coil sensitivity variation in an intermediate spatial domain to determine the additional weighting applied in the kernel regression. FDR involves a localized estimation of kernel weights by selectively choosing the regularization parameter as a function of the k-space location. An upper limit on the extent of regularization is estimated by matching an error bound derived using a Monte Carlo approach (called cross-over estimation) to the difference between k-spaces reconstructed with varying levels of regularization and the k-space reconstructed from a reference filter using GCV.
