Examples of uniform-penalty inversion of multiexponential relaxation data

When multiexponential relaxation data are inverted to give quasi-continuous distributions of relaxation times, the computed distribution is usually smoothed by means of an applied penalty function equal to a coefficient, C, times the integrated square of amplitude, slope, or curvature. When the distribution has a sharp peak and either a broad peak or long tail, smoothing with a fixed coefficient, C, widens the sharp peak and/or breaks up the broad peak or tail into two or more separate peaks. An iterative feedback procedure is used to generate a separate C value for each computed point in such a way as to give roughly equal contributions to the penalty function from each computed point. This permits adequate smoothing of broad features without oversmoothing sharp peaks. Examples are given for artificial data, for nuclear magnetic resonance in fluids in porous media, and for nuclear magnetic resonance in biological tissues.