Optimization of inverse algorithm for estimating the optical properties of biological materials using spatially-resolved diffuse reflectance

Determination of the optical properties from intact biological materials based on diffusion approximation theory is a complicated inverse problem, and it requires proper implementation of inverse algorithm, instrumentation and experiment. This article was aimed at optimizing the procedure of estimating the absorption and reduced scattering coefficients of turbid homogeneous media from spatially-resolved diffuse reflectance data. A diffusion model and the inverse algorithm were first validated by Monte Carlo simulations. Sensitivity analysis was performed to gain an insight into the relationship between the estimated parameters and the dependent variables in the inverse algorithm for improving the parameter estimation procedure. Three data transformation and the relative weighting methods were compared in the nonlinear least squares regression. It is found that the logarithm and integral data transformation and relative weighting methods greatly improve estimation accuracy with the relative errors of 10.4%, 10.7% and 11.4% for the absorption coefficient, and 6.6%, 7.0% and 7.1% for the reduced scattering coefficient, respectively. Further statistical analysis shows that the logarithm transformation and relative weighting methods give more reliable estimations of the optical parameters. To accurately estimate the optical parameters, it is important to study and quantify the characteristics and properties of the mathematical model and its inverse algorithm.