PET Image Reconstruction Using Mumford-Shah Regularization Coupled with L1Data Fitting

In positron emission tomography (PET) image reconstruction, regularization methods are usually considered to suppress noise effects in reconstructed images. In this paper, we model this reconstruction problem in a new variational framework where the Mumford-Shah (MS) regularization coupled with recently developed L¹ data fidelity term is adapted. In order to simplify the numerical computation, Ambrosio and Tortorelli\´s Gamma-convergence approximation is also employed to substitute the irregular parts (edge set) of MS functionals with the auxiliary smooth function. In numerical studies we compare our method with the "conventional" penalized least-square (PLS) algorithm with local nonquadratic Huber penalty. Results show both the feasibility and efficiency of the proposed algorithm