SPECT Reconstruction with a Transformed Attenuation Prototype at Multiple Levels

A variational model for SPECT reconstruction with a nonlinearly transformed attenuation prototype

“…Exemplarily, two reconstruction problems are presented that assume certain configurations in terms of a regularizing energy or the inclusion of further knowledge of the attenuation. The discussion then leads to a third problem, which is similar to the reconstruction model in [2], but imposes non-negativity on the radiation density, which leads to superior reconstruction results; see Figure 3.…”

“…[10, p. 87]. Analogous to [2] we choose a straightforward Tikhonov-type regularization. Such a regularization generally allows for small displacements, which is sufficient for our reconstruction set-up; see Figure 2.…”

“…At first, we recall the key features of the simultaneous reconstruction model as outlined in [2]. This model is based on a projection operator which is linear in the density and non-linear in the attenuation.…”

“…To overcome these difficulties, deformable attenuation prototype is considered. An affine linear deformation model has been suggested in [11] and a nonlinear free-form-based model has been suggested in [2].…”

“…The contribution of this paper is that we improve the reconstruction model of [2] by adding an additional non-negativity constraint on the density f and evaluate the model on simulated cardiac phantom data.…”