Corrections to linear methods for diffuse optical tomography using approximation error modelling

Linear reconstruction methods in diffuse optical tomography have been found to produce reasonable good images in cases in which the variation in optical properties within the medium is relatively small and a reference measurement with known background optical properties is available. In this paper we examine the correction of errors when using a first order Born approximation with an infinite space Green's function model as the basis for linear reconstruction in diffuse optical tomography, when real data is generated on a finite domain with possibly unknown background optical properties. We consider the relationship between conventional reference measurement correction and approximation error modelling in reconstruction. It is shown that, using the approximation error modelling, linear reconstruction method can be used to produce good quality images also in situations in which the background optical properties are not known and a reference is not available.