A Sparsity-Based Method for Blind Compensation of a Memoryless Nonlinear Distortion: Application to Ion-Selective Electrodes

In this paper, we propose a method for blind compensation of a memoryless nonlinear distortion. We assume as prior information that the desired signal admits a sparse representation in a transformed domain that should be known in advance. Then, given that a nonlinear distortion tends to generate signals that are less sparse than the desired one, our proposal is to build a compensating function model that gives rise to a maximally sparse signal. The implementation of this proposal has, as central elements, a criterion built upon an approximation of the ℓ₀-norm, the use of polynomial functions as compensating structures, and an optimization strategy based on sequential quadratic programming. We provide a theoretic analysis for an ℓ₀-norm criterion and results considering synthetic data. We also employ the method in an actual application related to chemical analysis via ion-selective electrode arrays.