Nuclear magnetic resonance (NMR) relaxation time and diffusion coefficient have long been playing an important role in the study of porous media such as biological systems,[1] food,[2] building materials[3]and reservoir rocks.[4] A recently developed technique to acquire the two-dimensional diffusion-relaxation (D-T2) distribution function separates oil (especially heavy oil) from water by striking diffusivity contrast in fluids while obtaining their T2 distributions.[5] As a result,the 2D distribution functions become powerful tools in well logging and laboratory core analysis.A two-dimensional inverse Laplace transform is required to extract the 2D distribution functions from the observed data.The inversion is a typical ill-posed problem[6] with smooth keels for the measurement of the relaxation time or the diffusion coefficient,and inverting a large data set of low signal-to-noise ratio (SNR) in a short time is a great challenge.