5,302 research outputs found
Adaptive mesh reconstruction: Total Variation Bound
We consider 3-point numerical schemes for scalar Conservation Laws, that are
oscillatory either to their dispersive or anti-diffusive nature. Oscillations
are responsible for the increase of the Total Variation (TV); a bound on which
is crucial for the stability of the numerical scheme. It has been noticed
(\cite{Arvanitis.2001}, \cite{Arvanitis.2004}, \cite{Sfakianakis.2008}) that
the use of non-uniform adaptively redefined meshes, that take into account the
geometry of the numerical solution itself, is capable of taming oscillations;
hence improving the stability properties of the numerical schemes.
In this work we provide a model for studying the evolution of the extremes
over non-uniform adaptively redefined meshes. Based on this model we prove that
proper mesh reconstruction is able to control the oscillations; we provide
bounds for the Total Variation (TV) of the numerical solution. We moreover
prove under more strict assumptions that the increase of the TV -due to the
oscillatory behaviour of the numerical schemes- decreases with time; hence
proving that the overall scheme is TV Increase-Decreasing (TVI-D)
Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints
We consider the bilevel optimisation approach proposed by De Los Reyes,
Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation
(TV) denoising model featuring for multiple noise distributions. In
applications, the use of databases (dictionaries) allows an accurate estimation
of the parameters, but reflects in high computational costs due to the size of
the databases and to the nonsmooth nature of the PDE constraints. To overcome
this computational barrier we propose an optimisation algorithm that by
sampling dynamically from the set of constraints and using a quasi-Newton
method, solves the problem accurately and in an efficient way
Image Restoration using Total Variation Regularized Deep Image Prior
In the past decade, sparsity-driven regularization has led to significant
improvements in image reconstruction. Traditional regularizers, such as total
variation (TV), rely on analytical models of sparsity. However, increasingly
the field is moving towards trainable models, inspired from deep learning. Deep
image prior (DIP) is a recent regularization framework that uses a
convolutional neural network (CNN) architecture without data-driven training.
This paper extends the DIP framework by combining it with the traditional TV
regularization. We show that the inclusion of TV leads to considerable
performance gains when tested on several traditional restoration tasks such as
image denoising and deblurring
A Second Order TV-type Approach for Inpainting and Denoising Higher Dimensional Combined Cyclic and Vector Space Data
In this paper we consider denoising and inpainting problems for higher
dimensional combined cyclic and linear space valued data. These kind of data
appear when dealing with nonlinear color spaces such as HSV, and they can be
obtained by changing the space domain of, e.g., an optical flow field to polar
coordinates. For such nonlinear data spaces, we develop algorithms for the
solution of the corresponding second order total variation (TV) type problems
for denoising, inpainting as well as the combination of both. We provide a
convergence analysis and we apply the algorithms to concrete problems.Comment: revised submitted versio
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