Estimation of individual spectral cone fundamentals from color-matching functions is a classical and longstanding problem in color science. In this paper we propose a novel method to carry out this estimation based on a linear optimization technique, employing an assumption of a priori knowledge of the retinal absorptance functions. The result is an estimation of the combined lenticular and macular filtration for an individual, along with the nine coefficients in the linear combination that relates their color-matching functions to their estimated spectral-cone fundamentals. We test the method on the individual Stiles and Burch color-matching functions and derive cone-fundamental estimations for different viewing fields and matching experiment repetition. We obtain cone-fundamental estimations that are remarkably similar to those available in the literature. This suggests that the method yields results that are close to the true fundamentals.