Multi-scale Variational Model Research Articles

Multiscale variation model and activity level estimation algorithm of the Earth's magnetic field based on wavelet packets

Abstract. We suggest a wavelet-based multiscale mathematical model of geomagnetic field variations. The model is particularly capable of reflecting the characteristic variation and local perturbations in the geomagnetic field during the periods of increased geomagnetic activity. Based on the model, we have designed numerical algorithms to identify the characteristic variation component as well as other components that represent different geomagnetic field activity. The substantial advantage of the designed algorithms is their fully automatic performance without any manual control. The algorithms are also suited for estimating and monitoring the activity level of the geomagnetic field at different magnetic observatories without any specific adjustment to their particular locations. The suggested approach has high temporal resolution reaching 1 min. This allows us to study the dynamics and spatiotemporal distribution of geomagnetic perturbations using data from ground-based observatories. Moreover, the suggested approach is particularly capable of discovering weak perturbations in the geomagnetic field, likely linked to the nonstationary impact of the solar wind plasma on the magnetosphere. The algorithms have been validated using the experimental data collected at the IKIR FEB RAS observatory network. Keywords. Magnetospheric physics (storms and substorms)

遥感图像条带噪声的多尺度变分模型去除

遥感图像条带噪声的多尺度变分模型去除

A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising

The total variation model proposed by Rudin, Osher and Fatemi performs very well for removing noise while preserving edges. However, it favors a piecewise constant solution in BV space which often leads to the staircase effect, and small details such as textures are often filtered out with noise in the process of denoising. To preserve the textures and eliminate the staircase effect, we improve the total variation model in this paper. This is accomplished by the following steps: (1) we define a new space of functions of fractional-order bounded variation called the BV α space by using the Grünwald–Letnikov definition of fractional-order derivative; (2) we model the structure of the image as a function belonging to the BV α space, and the textures in different scales as functions belonging to different negative Sobolev spaces. Thus, we propose a class of fractional-order multi-scale variational models for image denoising. (3) We analyze some properties of the fraction-order total variation operator and its conjugate operator. By using these properties, we develop an alternation projection algorithm for the new model and propose an efficient condition of the convergence of the algorithm. The numerical results show that the fractional-order multi-scale variational model can improve the peak signal to noise ratio of image, preserve textures and eliminate the staircase effect efficiently in the process of denoising.

Incoherence at heterogeneous interfaces

To describe the small scale defect structure of incoherent interfaces in an elastic bi-crystal, we consider a multiscale variational model composed of two parts: a bulk energy density W and a nonconvex interfacial energy density ψ that depends on the microscopic lattice mismatch at the grain boundary and the relative crystallographic normal. Mismatch is described using a referential coherence tensor that measures the relative misfit at the grain boundary and serves to couple the bulk elastic deformation of the grains to small scale defect structures at the interface. Minimizing this energy yields predictions for the distribution of defect microstructures at the interface as a function of grain size, elastic stiffness, and lattice mismatch. Calculations for a heterophase (01) / (01) interface in a two-dimensional bi-crystal system are presented.