Reverse differentiation and the inverse diffusion problem

A.J. Davies, B. Christianson, Laurence Dixon, R Roy, P. van der Zee

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


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 boundary output fluxes. A finite element model is proposed for the solution process and the problem is posed as a least squares optimisation problem. An important and costly part of optimisation processes is the calculation of gradients of the merit function. It has been shown that for such problems the reverse differentiation process can be implemented very efficiently with significant savings in both computation time and store. In this paper we show that the finite element optimisation process with reverse differentiation is ideally suited to the solution of the inverse diffusion problem.
Original languageEnglish
Pages (from-to)217-221
Number of pages5
JournalAdvances in Engineering Software
Issue number4
Publication statusPublished - Jun 1997


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