Uniform-penalty inversion of multiexponential decay data - II. Data spacing, T-2 data, systematic data errors, and diagnostics

The basic method of UPEN (uniform penalty inversion of multiexponential dec ay data) is given in an earlier publication (Borgia et al., J. Magn. Reson. 132, 65-77 (1998)), which also discusses the effects of noise, constraints , and smoothing on the resolution or apparent resolution of features of a c omputed distribution of relaxation times. UPEN applies negative feedback to a regularization penalty, allowing stronger smoothing for a broad feature than for a sharp line. This avoids unnecessarily broadening the sharp line and/or breaking the wide peak or tail into several peaks that the relaxatio n data do not demand to be separate. The experimental acid artificial data presented earlier were T-1 data, and all had fixed data spacings, uniform i n log-time. However, for T-2 data, usually spaced uniformly in linear time, or for data spaced in any manner, we have found that the data spacing does not enter explicitly into the computation. The present work shows the exte nsion of UPEN to T-2 data, including the averaging of data in windows and t he use of the corresponding weighting factors in the computation. Measures are implemented to control portions of computed distributions extending bey ond the data range. The input smoothing parameters in UPEN are normally fix ed, rather than data dependent. A major problem arises, especially at high signal-to-noise ratios, when UPEN is applied to data sets with systematic e rrors due to instrumental nonidealities or adjustment problems. For instanc e, a relaxation curve for a wide line can be narrowed by an artificial down ward bending of the relaxation curve. Diagnostic parameters are generated t o help identify data problems, and the diagnostics are applied in several e xamples, with particular attention to the meaningful resolution of two clos ely spaced peaks in a distribution of relaxation times. Where feasible, pro cessing with UPEN in nearly real time should help identify data problems wh ile further instrument adjustments can still be made. The need for the nonn egative constraint is greatly reduced in UPEN, and preliminary processing w ithout this constraint helps identify data sets for which application of th e non-negative constraint is too expensive in terms of error of fit for the data set to represent sums of decaying positive exponentials plus random n oise. (C) 2000 Academic Press.