3D multispectral imaging (MSI) corrects most distortion in MRI near metallic implants at the cost of prolonged scan time by phase encoding to resolve slice distortions. However, existing methods to accelerate 3D MSI do not exploit the redundancy of slice-phase encoding for the dominant on-resonance signal. A novel compact representation of 3D-MSI images based on a decomposition of on- and off-resonance via robust principal component analysis (RPCA) is introduced to exploit this redundancy in a calibration and model-free reconstruction and push the current limits of accelerated 3D MSI. A complementary randomized sampling strategy is used to vary undersampling in different spectral bins to enable the separation. Experiments with retrospective and prospective undersampling show comparable image quality between standard MSI images and 2.6-3.4-fold accelerated RPCA and improvement over bin-by-bin compressed sensing reconstruction.