Use of multiple data types in time-resolved optical absorption and scattering tomography

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Abstract
In Time-resolved Optical Absorption and Scattering Tomography (TOAST) the imaging problem is to reconstruct the coefficients of absorption (mu)a and scattering (mu)s of light in tissue given the time-dependent photon flux at the surface of the subject, resulting from ultrafast laser input pulses. This inverse problem is mathematically similar to the Electrical Impedance problem (EIT) but presents some unique features. In particular the necessity of searching in two solution spaces requires the use of multiple data types that are maximally uncorrelated with respect to the solution spaces. We developed an algorithm for TOAST that uses an iterative non-linear gradient descent method to minimize an appropriate error norm. The algorithm can work on multiple types of data and an important topic is the choice of the best data format to use. Usually the choice is integrated intensity and mean time- of-flight for the temporal domain data. In this paper we compare these data types with the use of higher order moments of the temporal distribution (variance, skew, kurtosis). We show that reliable results must take detailed account of the confidence limits on each data point. We demonstrate how the probability distribution function for photon propagation can be calculated so that the variance of any given measurement type can be derived.

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