Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
An introduction to the mathematical theory of inverse problems
An introduction to the mathematical theory of inverse problems
Convergence of an Iterative Method for Total Variation Denoising
SIAM Journal on Numerical Analysis
Nonstationary iterated Tikhonov regularization
Journal of Optimization Theory and Applications
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
SIAM Journal on Scientific Computing
On Semismooth Newton's Methods for Total Variation Minimization
Journal of Mathematical Imaging and Vision
Determining the locations and discontinuities in the derivatives of functions
Applied Numerical Mathematics
Two stable methods with numerical experiments for solving the backward heat equation
Applied Numerical Mathematics
Total variation blind deconvolution
IEEE Transactions on Image Processing
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The aim of this paper is to reconstruct a paleo mountain topography using a total variation (TV) regularization. A coupled system integrates the tectonic process with the surface process to simulate the evolution of a paleo mountain topography. The tectonic process and the surface process are described by a 3D convection-diffusion equation and a 2D convection-diffusion equation, respectively. We recover a piecewise smooth velocity field for the tectonic process as well as reconstruct a piecewise smooth mountain topography for the surface process using a TV regularization in an iterative fashion. The effects of the number of samples and of wavelengths on inversions are investigated. In our numerical experiments, we shall experience three difficulties: (I) recovering a large quantity of information from the limited amount of measurement data; (II) detecting sharp features; (III) choosing a properly initial guess value for a TV regularization. The numerical experiments show that a TV regularization is an efficient and stable algorithm.