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Total variation (TV) regularization, originally introduced by Rudin, Osher and Fatemi in the context of image denoising, has become widely used in the field of inverse problems. Two major directions of modifications of the original approach were proposed later on. The first concerns adaptive variants of TV regularization, the second focuses on higher-order TV models. In the present paper, we co...

This paper studies the total variation regularization with an L1 fidelity term (TV-L1) model for decomposing an image into features of different scales. We first show that the images produced by this model can be formed from the minimizers of a sequence of decoupled geometry subproblems. Using this result we show that the TV-L1 model is able to separate image features according to their scales,...

Recently Y. Meyer gave a characterization of the minimizer of the Rudin-OsherFatemi functional in terms of the -norm. In this work we generalize this result to regularization models with higher order derivatives of bounded variation. This requires us to define generalized -norms. We present some numerical experiments to support the theoretical considerations.

This paper studies the total variation regularization model with an L1 fidelity term (TV-L1) for decomposing an image into features of different scales. We first show that the images produced by this model can be formed from the minimizers of a sequence of decoupled geometry subproblems. Using this result we show that the TV-L1 model is able to separate image features according to their scales,...

In this paper an attempt is made to investigate the possible temporal correlation between heavy precipitation episodes and cosmic rays’ activity, on various time scales. Cosmic rays measurements are sparse and cover less extended periods than those of precipitation. Precipitation is largely influenced by local climatic and even physiographic conditions, while cosmic rays’ distribution is far mo...

Let Ω be an open subset of R where 2 ≤ n ≤ 7; we assume n ≤ 2 because the case n = 1 has been treated elsewhere (see [Alli]) and is quite different from the case n > 1; we assume n ≤ 7 is that our work will make use of the regularity theory for area minimizing hypersurfaces. Let F(Ω) = L1(Ω) ∩ L∞(Ω)). Suppose s ∈ F(Ω) and Suppose γ : R→ [0,∞) is locally Lipschitzian, positive on R ∼ {0} and zer...

We study variational methods of bounded variation type for the data analysis. Y. Meyer characterized minimizers of the Rudin-Osher-Fatemi functional in dependence of the G-norm of the data. These results and the follow up work on this topic are generalized to functionals defined on spaces of functions with derivatives of finite bounded variation. In order to derive a characterization of minimiz...

The class of bounded variation bvF (u, v) of fuzzy numbers introduced by [8] has been investigated further with the help of the generalized weighted mean matrix G(u, v). Imposing some restrictions on the matrix G(u, v), we have established it’s relation with different class of sequences such as our known classical sets, set of all statistically null difference sequences, Cesaro sequences etc. A...