New Dispersion-Compliant Bases (DCB) to perform Perfusion MRI deconvolution. The DCB improve performance regardless the presence and amount of dispersion. The DCB deconvolution outperforms oSVD and the state-of-the-art CPI and CPI + VTF. Dispersion detection based on the effective residue function estimated with DCB. DCB can be used as a pre-processing tool to characterize dispersion when detected.