Uniform Penalty inversion of two-dimensions NMR Relaxation data

The inversion of two-dimensional NMR Relaxation data requires the solu- tion of a őrst-kind Fredholm Integral equation with separate exponential kernels. We extend to two-dimensions the Uniform Penalty principle (Borgia et al. J. Magn. Res- onance, 1998) by proposing an algorithm based on Tikhonov regularization with local regularization parameters and nonnegative constraints. The local regularization terms are computed as the ratio between noise norm and a combination of local curvature and gradient values. The corresponding regularization problem is solved by Projected Newton iterations. Experiments show better reconstructions of peaks and ŕat areas compared to Tikhonov regularization with global regularization parameter.