The present invention has a magnetic resonance spectroscopic imaging (MRSI) method that allows collecting a complete spectroscopic image with one spectral dimension and up to three spatial dimensions in a single signal excitation. The method employs echo-planar spatial-spectral encoding combined with phase encoding interleaved into the echo-planar readout train and partial parallel imaging to reconstruct spatially localized absorption mode spectra. This approach enables flexible tradeoff between gradient and RF encoding to maximize spectral width and spatial resolution. Partial parallel imaging (e.g. SENSE or GRAPPA) is employed with this methodology to accelerate the phase encoding dimension. A preferred implementation is with the recently developed superresolution parallel MRI method, which accelerates along both the readout and phase encoding dimensions and thus enables particularly large spectral width and spatial resolution. The symmetrical k-space trajectory of this methodology is designed to compensate phase errors due to convolution of spatial and spectral encoding. This method is suitable for hyperpolarized MRSI, spatial mapping of the diffusion coefficients of biochemicals and functional MRI using quantitative mapping of water relaxation.