Map estimation of oxygen tension in retinal vessels with phosphorescence lifetime imaging

In phosphorescence lifetime imaging methods oxygen tension in retinal vessels has traditionally been indirectly determined from the estimates of intermediate variables whose noise-contaminated linear combinations are observed as phosphorescence intensity images. The classical least squares (LS) and regularized least squares (RLS) methods were used to obtain estimates of the intermediate variables. The estimates of the intermediate variables are then used to compute oxygen tension. The estimates of intermediate variables, however, do not yield an optimum estimate of oxygen tension due to its nonlinear dependence on the ratio of intermediate variables. Moreover, prior knowledge about the variables is very limited so that the level of noise cannot be reliably estimated, thereby affecting the automated choice of the regularization parameter in the RLS method. In this study the problem of optimally estimating oxygen tension in retinal vessels using the maximum a posteriori (MAP) criterion is addressed. For this purpose the conditional distribution of oxygen tension is derived given the phosphorescence lifetime imaging observations and model. The performance of MAP is compared with that of LS and the RLS methods using simulated data and its improved performance in the presence of different levels of noise is demonstrated.