An efficient Jacobian reduction method for diffuse optical image reconstruction

Matthew E Eames,Phaneendra K Yalavarthy,Hamid Dehghani,Brian W Pogue

doi:10.1364/oe.15.015908

Abstract

Model based image reconstruction in Diffuse Optical Tomography relies on both the numerical accuracy of the forward model as well as the computational speed and efficiency of the inverse model. Most model based image reconstruction algorithms rely on Newton type inversion methods, whereby the inverse of a large Jacobian is approximated. In this work we present an efficient Jacobian reduction method which takes into account the total sensitivity of the imaging domain to the measured boundary data. It is shown using numerical and phantom data that by removing regions within the inverse model whose contribution to the measured data is less than 1%, it has no significant effect upon the estimated inverse problem, but does provide up to a 14 fold improvement in computational time.

Highlights

Near-Infrared (NIR) Diffuse Optical Tomography (DOT) is a non-invasive imaging technique whereby NIR light between the wavelengths of 650nm and 900nm is injected into tissue using optical fibers at the surface of the volume of interest and the emergent light is measured at points along the same surface [1,2,3]
For the forward problem, depending on the imaging domain, geometry and size, a number of models based on the Radiative Transport Equation (RTE) have been developed [13,14,15]
Since the light in soft tissue becomes diffuse within a couple of scattering distances, diffusion based calculations using the Finite Element Method (FEM) have been employed extensively in the case of imaging thick tissues [2, 3, 16]

Summary

Introduction

Near-Infrared (NIR) Diffuse Optical Tomography (DOT) is a non-invasive imaging technique whereby NIR light between the wavelengths of 650nm and 900nm is injected into tissue using optical fibers at the surface of the volume of interest and the emergent light is measured at points along the same surface [1,2,3]. One can either use a regular pixel based reconstruction or a second mesh of the imaging volume, but these contain approximately half of the forward mesh nodes, typically 10,000, unknowns for a single parameter reconstruction when structural prior information is unavailable This implies that the Jacobian calculated which, in this instance relates intrinsic absorption to a change in the boundary data (log of the amplitude), will have a size of 240 × 10,000 which will need to be inverted. Through the use of simulated data as well as measured phantom data, it is shown that by efficient removal of nodes within the forward mesh which do not contribute more than 1% change in data, no loss in imaging accuracy is seen, whereas the computational speed of the algorithm can be improved by 14 folds This approach is shown to be memory efficient, as the size of the Jacobian matrix reduced by 4 fold, leading to 16 fold increase in the available memory. To show potential and expandability to more data types and larger parameter (e.g. spectral) reconstruction, the use of frequency domain experimental data from a multi-layered gelatin phantom is presented whereby both optical absorption and reduced scatter are reconstructed simultaneously using measured log amplitude and phase boundary data at 100 MHz

Theory

Jacobian reduction

Simulated breast model

Findings

Discussions and conclusions