MaxGIRF: Image reconstruction incorporating concomitant field and gradient impulse response function effects

PURPOSE: To develop and evaluate an improved strategy for compensating concomitant field effects in non‐Cartesian MRI at the time of image reconstruction. THEORY: We present a higher‐order reconstruction method, denoted as MaxGIRF, for non‐Cartesian imaging that simultaneously corrects off‐resonance, concomitant fields, and trajectory errors without requiring specialized hardware. Gradient impulse response functions are used to predict actual gradient waveforms, which are in turn used to estimate the spatiotemporally varying concomitant fields based on analytic expressions. The result, in combination with a reference field map, is an encoding matrix that incorporates a correction for all three effects. METHODS: The MaxGIRF reconstruction is applied to noiseless phantom simulations, spiral gradient‐echo imaging of an International Society for Magnetic Resonance in Medicine/National Institute of Standards and Technology phantom, and axial and sagittal multislice spiral spin‐echo imaging of a healthy volunteer at 0.55 T. The MaxGIRF reconstruction was compared against previously established concomitant field‐compensation and image‐correction methods. Reconstructed images are evaluated qualitatively and quantitatively using normalized RMS error. Finally, a low‐rank approximation of MaxGIRF is used to reduce computational burden. The accuracy of the low‐rank approximation is studied as a function of minimum rank. RESULTS: The MaxGIRF reconstruction successfully mitigated blurring artifacts both in phantoms and in vivo and was effective in regions where concomitant fields counteract static off‐resonance, superior to the comparator method. A minimum rank of 8 and 30 for axial and sagittal scans, respectively, gave less than 2% error compared with the full‐rank reconstruction. CONCLUSIONS: The MaxGIRF reconstruction simultaneously corrects off‐resonance, trajectory errors, and concomitant field effects. The impact of this method is greatest when imaging with longer readouts and/or at lower field strength.