We introduce variants of the variational image denoising method proposed by Blomgren et alinterpolates between totalvariation denoising and isotropic diffusion denoising. We study how parameter choices affect results and allow tuning between TV denoising and isotropic diffusion for respecting texture on one spatial scale while denoising features assumed to be noise on finer spatial scales. Furthermore, we prove existence and (where appropriate) uniqueness of minimizers. We consider both L 2 and L 1 data fidelity terms.
The accuracy of density measurements and position resolution in flash (40 ns) radiography of thick objects with 24 Gev/c protons is investigated. A global model fit to step wedge data is shown to give a good description spanning the periodic table. The parameters obtained from the step wedge data are used to predict transmission through the French Test Object (FTO), a test object of nested spheres, to a precision better than 1%. Multiple trials have been used to show that the systematic errors are less than 2%. Absolute agreement between the average radiographic measurements of the density and the known density is 1%. Spatial resolution has been measured to be 200 μm at the center of the FTO. These data verify expectations of the benefits provided by high energy hadron radiography for thick objects.
In the case of radiography of a cylindrically symmetric object, the Abel transform is useful for describing the tomographic measurement operator. The inverse of this operator is unbounded, so regularization is required for the computation of satisfactory inversions. We introduce the use of the total variation seminorm for this purpose, and prove the existence and uniqueness of solutions of the corresponding variational problem. We illustrate the effectiveness of the total-variation regularization with an example and comparison with the unregularized inverse and the H 1 regularized inverse.
We introduce a new, and quite general variational model for opinion dynamics based on pairwise interaction potentials and a range of opinion evolution protocols ranging from random interactions to global synchronous flows in the opinion state space. The model supports the concept of topic “coupling”, allowing opinions held by individuals to be changed via indirect interaction with others on different subjects. Interaction topology is governed by a graph that determines interactions. Our model, which is really a family of variational models, has, as special cases, many of the previously established models for the opinion dynamics. After introducing the model, we study the dynamics of the special case in which the potential is either a tent function or a constructed bell-like curve. We find that even in these relatively simple potential function examples there emerges interesting behavior. We also present results of preliminary numerical explorations of the behavior of the model to motivate questions that can be explored analytically.
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