Application of the Reduced Basis Method to Hyperspectral Diffuse Optical Tomography

Diffuse optical tomography (DOT), which uses low-energy laser light in the visible to near infrared range, has become a popular alternative to traditional medical imaging techniques such as x-ray, because it is non-ionizing and cost effective. Since DOT is especially effective in reconstructing images of soft tissue, where light penetrates more easily, one of its main applications is in breast cancer detection. Hyperspectral DOT (hyDOT) uses hundreds of optical wavelengths in the imaging process in order to improve the resolution of the image by adding new information. We develop a reduced basis method approach to solve the forward problem in hyDOT, which is to determine the measurements on the boundary of the tissue given information about the light source on the boundary, the location of any tumors, and the values of the absorption and diffusion coefficients. Our work on the forward problem is motivated by the image reconstruction problem in hyDOT which is computationally expensive because any algorithm requires solving the forward problem hundreds, if not thousands, of times. We show how the reduced basis method greatly improves the computational burden of the forward problem and thus, improves the efficiency of the reconstruction problem