In this paper, we investigate the total variation diminishing property for a class of 2-stage explicit Rung-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for (ODEs). Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious o...

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...

We examine the performance of Total Variation (TV) smoothing for processing of noisy Electrocardiogram (ECG) recorded by an ambulatory device. The TV smoothing is compared with traditionally-used bandpass filtering using ECG with artificially added noise, as well as with real-world noise obtained during physiological monitoring. The fundamental difference between TV smoothing and traditional ba...

The use of total variation as a regularization term in imaging problems was motivated by its ability to recover the image discontinuities.This is at the basis of its numerous applications to denoising, optical flow, stereo imaging and D surface reconstruction, segmentation, or interpolation to mention some of them. On one hand, we review here the main theoretical arguments that have been given...

Total variation regularization and anisotropic filtering have been established as standard methods for image denoising because of their ability to detect and keep prominent edges in the data. Both methods, however, introduce artifacts: In the case of anisotropic filtering, the preservation of edges comes at the cost of the creation of additional structures out of noise; total variation regulari...

We introduce a novel generic energy functional that we employ to solve inverse imaging problems within a variational framework. The proposed regularization family, termed as structure tensor total variation (STV), penalizes the eigenvalues of the structure tensor and is suitable for both grayscale and vector-valued images. It generalizes several existing variational penalties, including the tot...

Abstract. In this paper we analyze iterative regularization with the Bregman distance of the total variation semi norm. Moreover, we prove existence of a solution of the corresponding flow equation as introduced in [8] in a functional analytical setting using methods from convex analysis. The results are generalized to variational denoising methods with L-norm fit-to-data terms and Bregman dist...