<title>Imaging in diffusing media with a neural net formulation: a problem in large-scale computation</title>

Abstract

Abstract A neural network scheme is described, based on a modified backpropagation algorithm for the recovery of images of theinterior of objects which diffuse radiation. The method is capable of considering isotropic and any degree of forward directedscatter. The computational requirements of the method are significantly greater than for coherent (i.e. straight-line) based im-aging schemes and for this reason we have developed a machine architecture and machine, Kilonode. Results are shown for 2-D simulations of media having simple structure and can readily be extended to 3-D. Training vectors for the neural network arederived from time-independent and time-resolved signals. 1.0 Introduction Evaluation of the problem of imaging in diffusing media is particularly challenging both in regard to defining a suitablereconstruction algorithm and in terms of identifying an appropriate computing environment for efficient processing. In this pa-per we have examined both issues and, in particular, describe results of an algebraic technique for imaging the interior of ob-jects which diffuse penetrating radiation using a new multicomputer environment. The problem of imaging in diffusing mediadiffers significantly from other imaging schemes which rely on the detection of coherent signals in that we assume only prob-abilistic knowledge of the path of the radiation and minimal knowledge of the absorption profile of the medium. Because ofthis added uncertainty the size of the computation is unavoidably much greater than for coherent-based schemes and is an cx-ample of an ultra-large scale computing problem.Two important issues which arise when evaluating problems of this size are numerical precision and the overall comput-ing efficiency. Both must be considered simultaneously and involve trade-offs. Our approach has been that numerical precisionis paramount. In addition we have developed an operating system which evaluates algorithms in a manner which minimize thecommunication overhead. Because of the efficiency, the system we have developed can allow for the configuration of a largemultinode uniL A four-node system is currently available and operates at 320 Mflops. A 100 node system runs at 6400 Mflops,which is an efficiency of 80%. These efficiencies make it feasible and, in fact, desirable to employ numerically stable algo-rithms which, though computationally more intensive than others, can be evaluated in a time frame which readily permits thedevelopment of strategies for the solution of large scale computing problems.The algorithms we propose are more closely related to algebraic reconstruction algorithms such as ART, SIRT andSART than to algorithms based on the Born and Rytov approximations such as used for tomographic imaging with diffract-ing sources. In our model we assume that an NIR laser is used to provide the input radiation and suitable detectors are posi-tioned to measure both transmitted and backscatter signals. The present work considers a simple Markov process for the wayin which the energy propagates in the medium. It should be noted though, that the reconstruction technique we propose can useany model. Current simulations are in 2-D but are easily extended to 3-D. These studies were motivated by recent reports fromour group 2-4andothers, which showed promising results for imaging in dense scattering media given only diffusely scat-tered signals. A preliminary description of the findings has recently been reported. 8