Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography—part 2: image reconstruction

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. 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. Furthermore, structural information can be incorporated into the image reconstruction with PAD-WT to improve image quality and resolution. In this case, the weights used to average voxels in the image are calculated using the structural image, instead of the fluorescence image. The regularisation strength depends on both structural and fluorescence images, which guarantees that the method can preserve fluorescence information even when it is not structurally visible in the anatomical images. In part 1, we tested the method using a denoising problem. Here, we use simulated and in vivo mouse fDOT data to assess the algorithm performance. Our results show that the proposed PAD-WT method provides high quality and noise free images, superior to those obtained using AD.