Inverse problem for biomedical applications: use of prior information on target and forward model parameters

We propose the use of a retrieval operator for biomedical applications in near-infrared spectroscopy. The proposed retrieval operator is based on the "Optimal Estimation" method. The main characteristic of this method relates to the possibility to include prior information both on target and on forward model parameters of the inversion procedure. The possibility of the retrieval operator to elaborate a-priori information can in principle be a benefit for the whole retrieval procedure. This means that a larger number of target parameters can be retrieved, or that a better accuracy can be achieved in retrieving the target parameters. The final goal of this inversion procedure is to have an improved estimate of the target parameters. The procedure has been tested on time-resolved simulated experiments obtained with a Monte Carlo code. The results obtained show that an improved performance of the inversion procedure is achieved when prior information on target and forward model parameters is available. With the use of a priori information on target parameters we have in average a lower difference between the retrieved values of the parameters and their true values, and the error bars determined by the inversion procedure on the retrieved parameters are significantly lower. At the same time a good estimate of the errors on the forward model parameters can significantly improve the retrieval of the target parameters.