NonCartesian MR image reconstruction with integrated gradient nonlinearity correction

Purpose: To derive a noniterative gridding-type reconstruction framework for nonCartesian magnetic resonance imaging (MRI) that prospectively accounts for gradient nonlinearity (GNL)-induced image geometrical distortion during MR image reconstruction, as opposed to the standard, image-domain based GNL correction that is applied after reconstruction; to demonstrate that such framework is able to reduce the image blurring introduced by the conventional GNL correction, while still offering effective correction of GNL-induced geometrical distortion and compatibility with off-resonance correction. Methods: After introducing the nonCartesian MRI signal model that explicitly accounts for the effects of GNL and off-resonance, a noniterative gridding-type reconstruction framework with integrated GNL correction based on the type-III nonuniform fast Fourier transform (NUFFT) is derived. A novel type-III NUFFT implementation is then proposed as a numerically efficient solution to the proposed framework. The incorporation of simultaneous B0 off-resonance correction to the proposed framework is then discussed. Several phantom and in vivo data acquired via various 2D and 3D nonCartesian acquisitions, including 2D Archimedean spiral, 3D shells with integrated radial and spiral, and 3D radial sampling, are used to compare the results of the proposed and the standard GNL correction methods. Results: Various phantom and in vivo data demonstrate that both the proposed and the standard GNL correction methods are able to correct the coarse-scale geometric distortion and blurring induced by GNL and off-resonance. However, the standard GNL correction method also introduces blurring effects to corrected images, causing blurring of resolution inserts in the phantom images and loss of small vessel clarity in the angiography examples. On the other hand, the results after the proposed GNL correction show better depiction of resolution inserts and higher clarity of small vessel. Conclusions: The proposed GNL-integrated nonCartesian reconstruction method can mitigate the resolution loss that occurs during standard image-domain GNL correction, while still providing effective correction of coarse-scale geometric distortion and blurring induced by GNL and off-resonance.