Simultaneous reconstruction and segmentation for dynamic PET: A low rank framework

Accurate and robust activity map reconstruction from emission sinogram and segmentation of region of interest geometry for dynamic PET are of great technical challenges and significant clinical values. Traditionally, activity map reconstruction and boundary or volumetric segmentation problems are treated as two sequential steps. In this paper, we present an integrated, low-rank representation based scheme for the joint recovery of these two ill-posed problems at the same time. The resulting nuclear norm and l₁ norm related minimization problem can also be efficiently solved by many recently developed numerical methods. In this paper, the linearized alternating direction method is applied. Effectiveness of the proposed scheme is illustrated on two data sets: synthetic data and Monte Carlo simulations.