Regularisation and the inverse problem
In this paper the task of solving the inverse photon diffusion problem in human tissue will be discussed. In such problems the optical properties of the tissue are to be determined from a knowledge of measured values of the boundary output fluxes. Measurements are, of course, normally corrupted by noise. By using a finite element model of the diffusion process and simulated noise, it is shown that the estimates obtained by minimising the sum of squares of errors in the output fluxes are biased. Alternative objective functions are discussed that overcome this difficulty and are incidentally easier to minimise. A simple upper bound is given for the amount of noise that can be permitted if reliable estimates are to be obtained.
regularisation inverse problem diffusion problem finite element method