Modeling non‐stationarity of kernel weights for k‐space reconstruction in partially parallel imaging

Abstract

In partially parallel imaging, most k-space-based reconstruction algorithms such as GRAPPA adopt a single finite-size kernel to approximate the true relationship between sampled and nonsampled signals. However, the estimation of this kernel based on k-space signals is imperfect, and the authors are investigating methods dealing with local variation of k-space signals. To model nonstationarity of kernel weights, similar to performing a spatially adaptive regularization, the authors fit a set of linear functions using concepts from geographically weighted regression, a methodology used in geophysical analysis. Instead of a reconstruction with a single set of kernel weights, the authors use multiple sets. A missing signal is reconstructed with its kernel weights set determined by k-space clustering. Simulated and acquired MR data with several different image content and acquisition schemes, including MR tagging, were tested. A perceptual difference model (Case-PDM) was used to quantitatively evaluate the quality of over 1000 test images, and to optimize the parameters of our algorithm. A MOdeling Non-stationarity of KErnel wEightS ("MONKEES") reconstruction with two sets of kernel weights gave reconstructions with significantly better image quality than the original GRAPPA in all test images. Using more sets produced improved image quality but with diminishing returns. As a rule of thumb, at least two sets of kernel weights, one from low- and the other from high frequency k-space, should be used. The authors conclude that the MONKEES can significantly and robustly improve the image quality in parallel MR imaging, particularly, cardiac imaging.