Jason Peter Stockmann1, Robert Todd Constable2
1Biomedical Engineering, Yale University, New Haven, CT, USA; 2Diagnostic Radiology & Neurosurgery, Yale School of Medicine, and Biomedical Engineering, Yale University, New Haven, CT, USA
The Kaczmarz iterative algorithm (also known as Algebraic Reconstruction Technique, or ART) is applied to the problem of reconstructing images using arbitrary combinations of coil and gradient encoding. Methods have recently been proposed to form images using higher-order gradient encoding functions such as spherical harmonics. Since these encoding functions do not project the object into k-space, we propose to solve the MR signal equation directly without Fourier Transforming the echoes. Kaczmarz is used to reconstruct simulated data produced by linear and non-linear gradients, and spatially-varying point spread functions are illustrated.