相关论文: On the use of nonlinear regularization in inverse …

Inversions of rotational splittings have shown that there exists at the base of the solar convection zone a region called the tachocline in which high radial gradients of the rotation rate occur. The usual linear regularization methods tend…

Helioseismic inversions, carried out for several years on various ground-based and spatial observations, have shown that the solar rotation rate presents two principal regimes: a quasi-rigid rotation in the radiative interior and a…

A new set of accurately measured frequencies of solar oscillations are used to infer the rotation rate inside the Sun, as a function of radial distance as well as latitude. We have adopted a regularized least squares technique with…

We use rotation splittings derived from very long and long time series, namely 25.2, 12.6 and 6.3 year long, computed by Korzennik (2023) independent methodology to characterize the solar tachocline and its variation with latitude and time.…

We present a detailed numerical study of the Gough & McIntyre model for the solar tachocline. This model explains the uniformity of the rotation profile observed in the bulk of the radiative zone by the presence of a large-scale primordial…

Helioseismic inversions for the rotation rate have established the presence of a tachocline near the base of the solar convection zone. We show that the tachocline produces a characteristic oscillatory signature in the splitting…

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

Regularization in convolutional neural networks (CNNs) is usually addressed with dropout layers. However, dropout is sometimes detrimental in the convolutional part of a CNN as it simply sets to zero a percentage of pixels in the feature…

In this paper, we present a model for the effects of the tachocline on the differential rotation in the solar convection zone. The mathematical technique relies on the assumption that entropy is nearly constant ("well-mixed") in isorotation…

Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale. The associated inverse scale space flow can be obtained using the classical Bregman iteration applied to a convex,…

The solar tachocline, located at the interface between the latitude-dependent rotation of the convection zone and the rigid radiative interior, presents high gradients of angular velocity which are of particular interest for the models of…

Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale, induced by the choice of a convex, absolutely one-homogeneous regularizer. The associated inverse scale space flow can…

Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…

Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…

This paper develops a mathematical framework for interpreting observations of solar inertial waves in an idealized setting. Under the assumption of purely toroidal linear waves on the sphere, the stream function of the flow satisfies a…

Building on the well-known total-variation (TV), this paper develops a general regularization technique based on nonlinear isotropic diffusion (NID) for inverse problems with piecewise smooth solutions. The novelty of our approach is to be…

Helioseismology has provided very detailed inferences about rotation of the solar interior. Within the convection zone the rotation rate roughly shares the latitudinal variation seen in the surface differential rotation. The transition to…

We present a local but fully nonlinear model of the solar tachocline, using three-dimensional direct numerical simulations. The tachocline forms naturally as a statistically steady balance between Coriolis, pressure, buoyancy and Lorentz…

We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…

We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account…