Various embodiments accelerate high-resolution magnetic resonance spectroscopic imaging (MRSI). Various embodiments are built on a low-dimensional subspace model exploiting the partial separability of high-dimensional MRSI signals. For two and three dimensional MRSI with one spectral dimension, various embodiments sparsely sample the corresponding (k,t)-space in two complementary data sets, one with dense temporal sampling and high signal-to-noise ratio but limited k-space coverage and the other with sparse temporal sampling but extended k-space coverage. The reconstruction is then done by estimating a set of temporal/spectral basis functions and the corresponding spatial coefficients from these two data sets. The imaging technique of various embodiments can be used for high-resolution MRSI of different nuclei.