Algebraic reconstruction of images of a diffusive medium containing strong absorbers: Comparative study of different illumination schemes and the effect of restricted view angle

The quality of the answer computed by an image reconstruction algorithm could significantly depend on certain details of the data collection and analysis procedures. We describe some of the decisions that must be made during both of these steps, e.g. the geometry, number, and locations of both sources and detectors, selection of a set of time windows or modulation frequencies, and whether to process the data in a simultaneous or sequential manner. Because no set of choices is self-evidently optimal, we chose to use one comprehensive set of internal light intensity distributions and detector reading, both computed from Monte Carlo simulations, as a standard for tests of different varieties of image reconstruction algorithms applied to different subsets of detector readings. The reference medium in all cases was a densely scattering homogeneous, infinitely long cylinder. The three targets consisted of the same cylinder with the addition of either a single black absorbing rod on the axis, a single black absorbing rod parallel to the axis, or thirteen black absorbing rods distributed in the form of an 'X'. Time-resolved detector responses and internal collision densities were computed directly, and from these, time-independent and frequency domain data were subsequently calculated. Images were recontructed using algebraic algorithms that solve a system of linear perturbation equations that are valid only for sufficiently weak perturbations of the reference medium. Results shown compare images obtained using data from different domains and different sets of source locations. The quality of the one-absorber images is very good to excellent. The quality of the images of the thirteen-absorber target, for which the weak perturbation premise is very strongly voilated, is only fair. Sources of random and systematic errors are identified, and the effects of both types is discussed.