Jason Peter Stockmann1, Gigi Galiana2, Vicente Parot3,4, Leo Tam1, Robert Todd Constable1,2
1Biomedical Engineering, Yale University, New Haven, CT, USA; 2Diagnostic Radiology, Yale University, New Haven, CT, USA; 3Biomedical Imaging Center, Pontificia Universidad Catlica de Chile, Santiago, Chile; 4Department of Electrical Engineering, Pontificia Universidad Catlica de Chile, Santiago, Chile
The variable-order fractional Fourier transform (FrFT) is used to describe signals acquired using both linear and quadratic encoding gradients during readout. The FrFT is a generalization of the Fourier transform which imparts a rotation of angle α in time-frequency space. As quadratic phase evolves during readout, α changes continuously. We reconstruct images on a point-by-point basis using the variable-order FrFT for each α along with a radial k-space density compensation function. FrFT images show markedly reduced sensitivity to off-resonance phase and gradient calibration errors as compared with images reconstructed using an iterative brute force solver with the full encoding matrix.