Improvement of image quality of time-domain diffuse optical tomography with lp sparsity regularization

Shinpei Okawa,Yoko Hoshi,Yukio Yamada

doi:10.1364/boe.2.003334

Abstract

An lp (0 < p ≤ 1) sparsity regularization is applied to time-domain diffuse optical tomography with a gradient-based nonlinear optimization scheme to improve the spatial resolution and the robustness to noise. The expression of the lp sparsity regularization is reformulated as a differentiable function of a parameter to avoid the difficulty in calculating its gradient in the optimization process. The regularization parameter is selected by the L-curve method. Numerical experiments show that the lp sparsity regularization improves the spatial resolution and recovers the difference in the absorption coefficients between two targets, although a target with a small absorption coefficient may disappear due to the strong effect of the lp sparsity regularization when the value of p is too small. The lp sparsity regularization with small p values strongly localizes the target, and the reconstructed region of the target becomes smaller as the value of p decreases. A phantom experiment validates the numerical simulations.

Highlights

Diffuse optical tomography (DOT) reconstructs the distributions of the optical properties, such as the scattering and absorption coefficients in the biological media
To improve the spatial resolution and the robustness to noise, the lp (0 < p ≤ 1) sparsity regularization is applied to the time-domain diffuse optical tomography with the gradient-based nonlinear optimization scheme
The expression of the lp sparsity regularization is reformulated as a differentiable function of a parameter to avoid the difficulty in calculating its gradient in the optimization process

Summary

Introduction

Diffuse optical tomography (DOT) reconstructs the distributions of the optical properties, such as the scattering and absorption coefficients in the biological media. By solving the inverse problem based on the photon diffusion equation with the measurement data of the detected light, DOT images are obtained noninvasively [1, 2]. The reconstructed optical properties contain the information about the structure but. The advantage of the near infrared optical imaging modalities is that the measuring instruments are smaller in size and easier to use than the other modalities. When the number of the detectors is limited, the inverse problem of DOT is highly ill-posed. One of the solutions of these problems is to use a regularization method in the image reconstruction. Recently the regularization techniques are actively studied for improvement of the DOT image quality

Methods

Results

Conclusion