Regularization lemmas and convergence in total variation

Total Variation Regularization in

We propose computational algorithms for incorporating total varia-tional (TV) regularization in positron emission tomography (PET). The motivation for using TV is that it has been shown to suppress noise effectively while capturing sharp edges without oscillations. This feature makes it particularly attractive for those applications of PET where the objective is to identify the shape of objects...

Total Variation Regularization in Electrical Impedance Tomography

This paper presents an evaluation of the use of Primal Dual Methods for efficiently regularizing the electric impedance tomography (EIT) problem with the Total Variation (TV) functional. The Total Variation functional is assuming an important role in the regularization of inverse problems thanks to its ability to preserve discontinuities in reconstructed profiles. This property is desirable in ...

Total Variation Regularization in PET Reconstruction

Positron Emission Tomography reconstruction is ill posed. The result obtained with iterative maximum likelihood estimation has maximum probability, but is often unrealistic and has noisy behavior. The introduction of additional knowledge in the solution process is called regularization. Common regularization methods enforce continuity, smoothness or finite band-limits, but these are inappropria...

Total-Variation Regularization in Positron Emission Tomography

Discrete Total Variation Flows without Regularization

We propose and analyze an algorithm for the solution of the L2-subgradient flow of the total variation functional. The algorithm involves no regularization, thus the numerical solution preserves the main features that motivate practitioners to consider this type of energy. We propose an iterative scheme for the solution of the arising problems, show that the iterations converge, and develop a s...