Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography—part 1: technical principles

Abstract

Fluorescence diffuse optical tomography (fDOT) provides 3D images of fluorescence distributions in biological tissue, which represent molecular and cellular processes. The image reconstruction problem is highly ill-posed and requires regularisation techniques to stabilise and find meaningful solutions. Quadratic regularisation tends to either oversmooth or generate very noisy reconstructions, depending on the regularisation strength. Edge preserving methods, such as anisotropic diffusion regularisation (AD), can preserve important features in the fluorescence image and smooth out noise. However, AD has limited ability to distinguish an edge from noise. In this two-part paper, we propose a patch-based anisotropic diffusion regularisation (PAD), where regularisation strength is determined by a weighted average according to the similarity between patches around voxels within a search window, instead of a simple local neighbourhood strategy. However, this method has higher computational complexity and, hence, we wavelet compress the patches (PAD-WT) to speed it up, while simultaneously taking advantage of the denoising properties of wavelet thresholding. The proposed method combines the nonlocal means (NLM), AD and wavelet shrinkage methods, which are image processing methods. Therefore, in this first paper, we used a denoising test problem to analyse the performance of the new method. Our results show that the proposed PAD-WT method provides better results than the AD or NLM methods alone. The efficacy of the method for fDOT image reconstruction problem is evaluated in part 2.