Pre-processing method to improve optical parameters estimation in Monte Carlo-based inverse problem solving

Determining the optical properties of biological tissues in vivo from spectral intensity measurements performed at their surface is still a challenge. Based on spectroscopic data acquired, the aim is to solve an inverse problem, where the optical parameter values of a forward model are to be estimated through optimization procedure of some cost function. In many cases it is an ill-posed problem because of small numbers of measures, errors on experimental data, nature of a forward model output data, which may be affected by statistical noise in the case of Monte Carlo (MC) simulation or approximated values for short inter-fibre distances (for Diffusion Equation Approximation (DEA)). In case of optical biopsy, spatially resolved diffuse reflectance spectroscopy is one simple technique that uses various excitation-toemission fibre distances to probe tissue in depths. The aim of the present contribution is to study the characteristics of some classically used cost function, optimization methods (Levenberg-Marquardt algorithm) and how it is reaching global minimum when using MC and/or DEA approaches. Several methods of smoothing filters and fitting were tested on the reflectance curves, I(r), gathered from MC simulations. It was obtained that smoothing the initial data with local regression weighted second degree polynomial and then fitting the data with double exponential decay function decreases the probability of the inverse algorithm to converge to local minima close to the initial point of first guess.