Accelerated three‐dimensional multispectral MRI with robust principal component analysis for separation of on‐ and off‐resonance signals

Purpose To enable highly accelerated distortion-free MRI near metal by separating on- and off-resonance to exploit the redundancy of slice-phase encoding for the dominant on-resonance component. Methods Multispectral MRI techniques resolve off-resonance distortions by a combination of limited excitation bins and additional encoding. Inspired by robust principal component analysis, a novel compact representation of multispectral images as a sum of rank-one and sparse matrices corresponding to on- and off-resonance respectively is described. This representation is used in a calibration-free and model-free reconstruction for data with an undersampling pattern that varies between bins. Retrospective undersampling was used to compare the proposed reconstruction and bin-by-bin compressed sensing. Hip images were acquired in eight patients with standard and prospectively undersampled three-dimensional multispectral imaging, and image quality was evaluated by two radiologists on a 5-point scale. Results Experiments with retrospective undersampling showed that the enhanced sparsity afforded by the separation greatly reduces reconstruction errors and artifacts. Images from prospectively undersampled multispectral imaging offered 2.6–3.4-fold (18–24-fold overall) acceleration compared to standard multispectral imaging with parallel imaging and partial-Fourier acceleration with equivalence in all qualitative assessments within a tolerance of one point (P < 0.004). Conclusion Three-dimensional multispectral imaging can be highly accelerated by varying undersampling between bins and separating on- and off-resonance. Magn Reson Med, 2017. © 2017 International Society for Magnetic Resonance in Medicine.