Robust anisotropic diffusion prior with anatomical regularization for 3D SPECT reconstruction

In this study, we aim at reconstructing single photon emission computed tomography (SPECT) images with the employment of available anatomical data. We use an anatomically weighted anisotropic median diffusion filter (AWAMDF) as a regularization term in a maximum a posteriori (MAP) framework. In the proposed method, co-registered data from magnetic resonance (MR) is embedded directly into the robust diffusion update equation to encourage anatomically adaptive local diffusion flow and noise suppression. The main aim of this study is to present a possible way to determine pathological tissues, such as hot and cold lesions, apparent only on emission data, while preserving edges from the anatomical image. Aiming to detect boundaries on highly distorted data, we use a Tukey's Biweight error norm in the framework of robust diffusion with a special constraint on the local gradient. Quantitative assessment of AWAMDF is performed using simulated 3D SPECT/MR data, and compared with Bowsher prior. AWAMDF outperforms BP quantitatively for damaged brain areas, and with slightly inferior variance for the whole gray matter region. (orig.)