An inequality-constrained least-squares deconvolution method

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Abstract
The output-function (Y) of a linear system is the convolution of the input function (I) to the system with the disposition-function (H) of the system. Given Y and H deconvolution yields I. A non-parametric method for numerical deconvolution is described. The method is based on an inequality-constrained least-squares criterion and approximates I by a discontinuous function. No assumptions are made about the form of H or Y. Numerical stability and physical realism are obtained by constraining the estimated I to be nonnegative and piecewise-monotonic (nonincreasing, nondecreasing, or alternating segments of both). When I is constrained to be monotonic, the deconvolution yields a staircase function. The method can be used to calculate drug input rates. It is compared to previously published deconvolution methods for this purpose, using simulated data and real theophylline and pentobarbital data.