Quasi-Newton methods in iterative image reconstruction for optical tomography

Optical Tomography (OT) can provide useful information about the interior distribution of optical properties in various body parts, such as the brain, breast, or finger joints. This novel medical imaging modality uses measured transmission intensities of near infrared light that are detected on accessible surfaces. Image reconstruction schemes compute from the measured data cross sectional images of the optical properties throughout the body. The image quality and the computational speed largely depend on the employed reconstruction method. Of considerable interest are currently so-called model-based iterative image reconstruction schemes, in which the reconstruction problem is formulated as an optimization problem. The correct image equals the spatial distribution of optical properties that leads to a minimum of a user-defined objective function. In the past several groups have developed steepest-gradient-descent (SGD) techniques and conjugate-gradient (CG) methods, which start from an initial guess and search for the minimum. These methods have shown some good initial results, however, they are known to be only slowly converging. To alleviate this disadvantage we have implemented in this work a quasi-Newton (QN) method. We present numerical results that show that QN algorithms are superior to CG techniques, both in terms of conversion time and image quality.