The invention consists of three image-postprocessing phases for the purposes of generating high-quality quantitative MR images (proton density (PD), T1, and T2) as well as high-quality virtual MR images with continuously adjustable computer-synthesized contrast weightings, from source images acquired directly with an MRI scanner. Each of the image-postprocessing phases uses one or several new computer algorithms that improve image quality with respect to prior art, including linear-combination-of source-images (LCSI) algorithms for generating PD images and model-conforming algorithms for generating Q-MR images of tissue properties that influence NMR relaxation.