444 research outputs found
Weighted structure tensor total variation for image denoising
Based on the variational framework of the image denoising problem, we
introduce a novel image denoising regularizer that combines anisotropic total
variation model (ATV) and structure tensor total variation model (STV) in this
paper. The model can effectively capture the first-order information of the
image and maintain local features during the denoising process by applying the
matrix weighting operator proposed in the ATV model to the patch-based Jacobian
matrix in the STV model. Denoising experiments on grayscale and RGB color
images demonstrate that the suggested model can produce better restoration
quality in comparison to other well-known methods based on
total-variation-based models and the STV model
Continuum-kinematics-inspired peridynamics. Mechanical problems
The main objective of this contribution is to develop a novel continuum-kinematics-inspired approach for peridynamics (PD), and to revisit PD’s thermodynamic foundations. We distinguish between three types of interactions, namely, one-neighbour interactions, two-neighbour interactions and three-neighbour interactions. While one-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism, two- and three-neighbour interactions are fundamentally different to state-based interactions in that the basic elements of continuum kinematics are preserved exactly. In addition, we propose that an externally prescribed traction on the boundary of the continuum body emerges naturally and need not vanish. This is in contrast to, but does not necessarily violate, standard PD. We investigate the consequences of the angular momentum balance and provide a set of appropriate arguments for the interactions accordingly. Furthermore, we elaborate on thermodynamic restrictions on the interaction energies and derive thermodynamically-consistent constitutive laws through a Coleman–Noll-like procedure
A High-Order Numerical Method for the Nonlinear Helmholtz Equation in Multidimensional Layered Media
We present a novel computational methodology for solving the scalar nonlinear
Helmholtz equation (NLH) that governs the propagation of laser light in Kerr
dielectrics. The methodology addresses two well-known challenges in nonlinear
optics: Singular behavior of solutions when the scattering in the medium is
assumed predominantly forward (paraxial regime), and the presence of
discontinuities in the % linear and nonlinear optical properties of the medium.
Specifically, we consider a slab of nonlinear material which may be grated in
the direction of propagation and which is immersed in a linear medium as a
whole. The key components of the methodology are a semi-compact high-order
finite-difference scheme that maintains accuracy across the discontinuities and
enables sub-wavelength resolution on large domains at a tolerable cost, a
nonlocal two-way artificial boundary condition (ABC) that simultaneously
facilitates the reflectionless propagation of the outgoing waves and forward
propagation of the given incoming waves, and a nonlinear solver based on
Newton's method.
The proposed methodology combines and substantially extends the capabilities
of our previous techniques built for 1Dand for multi-D. It facilitates a direct
numerical study of nonparaxial propagation and goes well beyond the approaches
in the literature based on the "augmented" paraxial models. In particular, it
provides the first ever evidence that the singularity of the solution indeed
disappears in the scalar NLH model that includes the nonparaxial effects. It
also enables simulation of the wavelength-width spatial solitons, as well as of
the counter-propagating solitons.Comment: 40 pages, 10 figure
Visco-potential free-surface flows and long wave modelling
In a recent study [DutykhDias2007] we presented a novel visco-potential free
surface flows formulation. The governing equations contain local and nonlocal
dissipative terms. From physical point of view, local dissipation terms come
from molecular viscosity but in practical computations, rather eddy viscosity
should be used. On the other hand, nonlocal dissipative term represents a
correction due to the presence of a bottom boundary layer. Using the standard
procedure of Boussinesq equations derivation, we come to nonlocal long wave
equations. In this article we analyse dispersion relation properties of
proposed models. The effect of nonlocal term on solitary and linear progressive
waves attenuation is investigated. Finally, we present some computations with
viscous Boussinesq equations solved by a Fourier type spectral method.Comment: 29 pages, 13 figures. Some figures were updated. Revised version for
European Journal of Mechanics B/Fluids. Other author's papers can be
downloaded from http://www.lama.univ-savoie.fr/~dutyk
Variational image denoising with adaptive constraint sets
Abstract. We propose a generalization of the total variation (TV) minimization method proposed by Rudin, Osher and Fatemi. This generalization allows for adaptive regularization, which depends on the minimizer itself. Existence theory is provided in the framework of quasi-variational inequalities. We demonstrate the usability of our approach by considering applications for image and movie denoising
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