Andreas Hielscher, Columbia University

It is well known that transport-theory-based reconstruction algorithms provide the most accurate reconstruction results in optical tomographic imaging. However, these codes require large amounts of memory and are usually slowly converging. To overcome these problems we have developed algorithms that employ PDE-constrained methods. These algorithms cover the cases of continuous-wave and frequency-domain tomography as well as fluorescence and bioluminescence problems. We have evaluated the performance of these various PDE-constrained schemes with numerical and experimental data and have found that the computation and memory requirement can be considerably reduced without affecting the accuracy of the solutions. These codes have successfully been applied in first clinical studies involving arthritis, diabetic, and breast-cancer patients.