Quantification and normalization of noise variance with sparsity regularization to enhance diffuse optical tomography

Abstract

Conventional reconstruction of diffuse optical tomography (DOT) is based on the Tikhonov regularization and the white Gaussian noise assumption. Consequently, the reconstructed DOT images usually have a low spatial resolution. In this work, we have derived a novel quantification method for noise variance based on the linear Rytov approximation of the photon diffusion equation. Specifically, we have implemented this quantification of noise variance to normalize the measurement signals from all source-detector channels along with sparsity regularization to provide high-quality DOT images. Multiple experiments from computer simulations and laboratory phantoms were performed to validate and support the newly developed algorithm. The reconstructed images demonstrate that quantification and normalization of noise variance with sparsity regularization (QNNVSR) is an effective reconstruction approach to greatly enhance the spatial resolution and the shape fidelity for DOT images. Since noise variance can be estimated by our derived expression with relatively limited resources available, this approach is practically useful for many DOT applications.