Constrained Numerical Deconvolution Using Orthogonal Polynomials

In this article, we present a novel extension of Cutler's deconvolution method to address the limitations of the original algorithm in estimating realistic input 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 extends Cutler's algorithm by incorporating  constraints using a ridge factor and Lagrangian multipliers in an iterative fashion. This extension maintains the iterative projection-based nature of the original method, avoiding the need for optimization solvers to perform constrained optimization. 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 provides physically plausible solutions compared to the original Cutler algorithm, as well as other widely known deconvolution techniques.