Robust principal component analysis for separation of on and off-resonance in 3D multispectral MRI

Accelerated 3D multispectral imaging (MSI) on a magnetic resonance imaging (MRI) system uses phase-encoding in two dimensions and frequency-encoding in the third. The method generates randomized k-space undersampling patterns that vary between different spectral bins to determine k-space samples to be acquired in each spectral bin; orders k-space samples into echo trains that determine gradient waveforms; initializes the gradient waveforms, RF waveforms, and timing information; plays the gradient and RF waveforms using the timing information to excite and refocus different spatial and spectral bin regions; acquires undersampled MRI signal data on the MRI system from the spatial and spectral bin regions; uses robust principal component analysis to reconstruct on-resonance images and off-resonance images represented as sets of low rank and sparse matrices from the undersampled MRI signal data; combines the on-resonance images and off-resonance images to yield a final image; and presents the final image on a display.