Modification of the normalized difference method for real-time optical tomography

Abstract

Computation-saving techniques and stability-adding techniques provide for fast, accurate reconstructions of a time series of images involving large-scale 3D problems, such as real-time image recovery in an optical tomography imaging system. A system equation for a target medium () such as tissue is solved using a Normalized Difference Method (NDM) (). Because of the inherent stability of the NDM solutions, a weight matrix (W) of the system equation can be provided for a given point in a time series (), then reused without recalculation at subsequent points. Further savings are achieved by decomposing W using singular value decomposition or direct matrix decomposition, transforming it to reduce its dimensions, and/or scaling it to achieve a more stable numerical solution. Values of measured energy () emerging from the target medium are back-substituted into the system equation for the different points to obtain the target medium properties.