86 research outputs found
Ancient Documents Denoising and Decomposition Using Aujol and Chambolle Algorithm
With the improvement of printing technology since the 15th century, there is a huge amount of printed documents published and distributed. These documents are degraded by the time and require to be preprocessed before being submitted to image indexing strategy, in order to enhance the quality of images. This paper proposes a new pre-processing that permits to denoise these documents, by using a Aujol and Chambolle algorithm. Aujol and Chambolle algorithm allows to extract meaningful components from image. In this case, we can extract shapes, textures and noise. Some examples of specific processings applied on each layer are illustrated in this paper
ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
On a coupled PDE model for image restoration
In this paper, we consider a new coupled PDE model for image restoration.
Both the image and the edge variables are incorporated by coupling them into
two different PDEs. It is shown that the initial-boundary value problem has
global in time dissipative solutions (in a sense going back to P.-L. Lions),
and several properties of these solutions are established. This is a rough
draft, and the final version of the paper will contain a modelling part and
numerical experiments
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