We propose a new multidimensional MRI experiment called T1 Relaxation-T2 Relaxation Correlation Spectroscopic Imaging (RR-CSI) for probing microstructure. RR-CSI acquires imaging data with two-dimensional relaxation contrast encoding and estimates a high-dimensional spectroscopic image by using spatially-constrained reconstruction. The spectroscopic image comprises a full 2D T1-T2 spectrum at every voxel. The distinct peaks in these spectra correspond to different microscopic tissue compartments, which enables spatial mapping of microstructure. Compared to conventional methods, RR-CSI has improved capabilities for resolving tissue microenvironments with similar relaxation parameters. RR-CSI is demonstrated with real MRI data, including the first in vivo human brain results.