Constrained numerical deconvolution using orthogonal polynomials

Abstract

In this article, we present an enhanced version of Cutler's deconvolution method to address the limitations of the original algorithm in estimating realistic input and output parameters. Cutler's method, based on orthogonal polynomials, suffers from unconstrained solutions, leading to the lack of realism in the deconvolved signals in some applications. Our proposed approach incorporates constraints using a ridge factor and Lagrangian multipliers in an iterative fashion, maintaining Cutler's iterative projection-based nature. This extension avoids the need for external optimization solvers, making it particularly suitable for applications requiring constraints on inputs and outputs. We demonstrate the effectiveness of the proposed method through two practical applications: the estimation of COVID-19 curves and the study of mavoglurant, an experimental drug. Our results show that the extended method presents a sum of squared residuals in the same order of magnitude of that of the original Cutler's method and other widely known unconstrained deconvolution techniques, but obtains instead physically plausible solutions, correcting the errors introduced by the alternative methods considered, as illustrated in our case studies.