Multidimensional MRI is an emerging approach that simultaneously encodes water relaxation (T1andT2) and mobility (diffusion) and replaces voxel-averaged values with subvoxel distributions of those MR properties. While conventional (i.e., voxel-averaged) MRI methods cannot adequately quantify the microscopic heterogeneity of biological tissue, using subvoxel information allows to selectively map a specificT1-T2-diffusion spectral range that corresponds to a group of tissue elements. The major obstacle to the adoption of rich, multidimensional MRI protocols for diagnostic or monitoring purposes is the prolonged scan time. Our main goal in the present study is to evaluate the performance of a nonlocal estimation of multispectral magnitudes (NESMA) filter on reduced datasets to limit the total acquisition time required for reliable multidimensional MRI characterization of the brain. Here we focused and reprocessed results from a recent study that identified potential imaging biomarkers of axonal injury pathology from the joint analysis of multidimensional MRI, in particular voxelwiseT1-T2and diffusion-T2spectra in human Corpus Callosum, and histopathological data. We tested the performance of NESMA and its effect on the accuracy of the injury biomarker maps, relative to the co-registered histological reference. Noise reduction improved the accuracy of the resulting injury biomarker maps, while permitting data reduction of 35.7 and 59.6% from the full dataset forT1-T2and diffusion-T2cases, respectively. As successful clinical proof-of-concept applications of multidimensional MRI are continuously being introduced, reliable and robust noise removal and consequent acquisition acceleration would advance the field towards clinically-feasible diagnostic multidimensional MRI protocols.