Three-dimensional total variation norm for SPECT reconstruction

The total variation (TV) norm has been described in literature as a method for reducing noise in two-dimensional (2D) images. At the same time. the TV -norm is very good at recovering edges in images, without introducing ringi ng or edge artefacts. It has also been proposed as a 2D regularisation func tion in Bayesian reconstruction, implemented in an expectation maximisation (EM) algorithm, and called TV-EM. The TV-EM was developed for 2D SPECT ima ging, and the algorithm is capable of smoothing noise while maintaining edg es without introducing artefacts. We have extended the TV-norm to take into account the third spatial dimension, and developed an iterative EM algorit hm based on the three-dimensional (3D) TV-norm, which we call TV3D-EM. This takes into account the correlation between transaxial sections in SPECT, d ue to system resolution. We have compared the 2D and 3D algorithms using re constructed images from simulated projection data. Phantoms used were a hom ogeneous sphere, and a 3D head phantom based on the Shepp-Logan phantom. Th e TV3D-EM algorithm yielded somewhat lower noise levels than TV-EM. The noi se in the TV3D-EM had similar correlation in transaxial and longitudinal se ctions, which was not the case for TV-EM, or any 2D reconstruction method. In particular, longitudinal sections from TV3D-EM were perceived as less no isy when compared to TV-EM. The use of 3D reconstruction should also be adv antageous if compensation for distant dependent collimator blurring is inco rporated in the iterative algorithm. (C) 2001 Elsevier Science B.V. All rig hts reserved.