Image reconstruction incorporating maxwell fields and gradient impulse response function distortion

A method for reconstructing a magnetic resonance imaging (MRI) image using an MRI system having symmetric x and y gradient coils, the method comprising:

• obtaining, by the MRI system, MRI data including k-space data of a patient;
• applying a convolution of inputted nominal gradient waveforms with a gradient impulse response function (GIRF) to determine predicted or distorted gradient waveforms produced by the symmetric x and y gradient coils of the MRI system, wherein GIRF measurements are acquired without using a field monitoring device, a field camera or field probes;
• calculating or determining, by the MRI system, linear Fourier terms of the k-space data and concomitant field terms arising from the predicted or distorted gradient waveforms without imposing approximations on k-space trajectories when calculating or determining concomitant field terms;
• calculating or determining, by the MRI system, an image vector or matrix by solving a cost function that describes the relationship between the captured or obtained k-space data and an image using a conjugate gradient algorithm or an iterative solver and a computational routine for the linear Fourier terms;
• and
• reconstructing, by the MRI system, an MRI image using the approximation-free concomitant field terms, the predicted or distorted gradient waveforms calculated with GIRFs, a measured field map or a static off-resonance map, and the image vector or matrix;
• and
• providing, by the MRI system, the reconstructed MRI image to a user.