1,179 research outputs found
Finite-time blowup for a complex Ginzburg-Landau equation with linear driving
In this paper, we consider the complex Ginzburg--Landau equation on , where
, and . By convexity
arguments we prove that, under certain conditions on ,
a class of solutions with negative initial energy blows up in finite time
Restoration of Poissonian Images Using Alternating Direction Optimization
Much research has been devoted to the problem of restoring Poissonian images,
namely for medical and astronomical applications. However, the restoration of
these images using state-of-the-art regularizers (such as those based on
multiscale representations or total variation) is still an active research
area, since the associated optimization problems are quite challenging. In this
paper, we propose an approach to deconvolving Poissonian images, which is based
on an alternating direction optimization method. The standard regularization
(or maximum a posteriori) restoration criterion, which combines the Poisson
log-likelihood with a (non-smooth) convex regularizer (log-prior), leads to
hard optimization problems: the log-likelihood is non-quadratic and
non-separable, the regularizer is non-smooth, and there is a non-negativity
constraint. Using standard convex analysis tools, we present sufficient
conditions for existence and uniqueness of solutions of these optimization
problems, for several types of regularizers: total-variation, frame-based
analysis, and frame-based synthesis. We attack these problems with an instance
of the alternating direction method of multipliers (ADMM), which belongs to the
family of augmented Lagrangian algorithms. We study sufficient conditions for
convergence and show that these are satisfied, either under total-variation or
frame-based (analysis and synthesis) regularization. The resulting algorithms
are shown to outperform alternative state-of-the-art methods, both in terms of
speed and restoration accuracy.Comment: 12 pages, 12 figures, 2 tables. Submitted to the IEEE Transactions on
Image Processin
Hamiltonian elliptic dynamics on symplectic 4-manifolds
We consider C2 Hamiltonian functions on compact 4-dimensional symplectic
manifolds to study elliptic dynamics of the Hamiltonian flow, namely the
so-called Newhouse dichotomy. We show that for any open set U intersecting a
far from Anosov regular energy surface, there is a nearby Hamiltonian having an
elliptic closed orbit through U. Moreover, this implies that for far from
Anosov regular energy surfaces of a C2-generic Hamiltonian the elliptic closed
orbits are generic.Comment: 9 page
Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization
Multiplicative noise (also known as speckle noise) models are central to the
study of coherent imaging systems, such as synthetic aperture radar and sonar,
and ultrasound and laser imaging. These models introduce two additional layers
of difficulties with respect to the standard Gaussian additive noise scenario:
(1) the noise is multiplied by (rather than added to) the original image; (2)
the noise is not Gaussian, with Rayleigh and Gamma being commonly used
densities. These two features of multiplicative noise models preclude the
direct application of most state-of-the-art algorithms, which are designed for
solving unconstrained optimization problems where the objective has two terms:
a quadratic data term (log-likelihood), reflecting the additive and Gaussian
nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a
total variation or wavelet-based regularizer/prior). In this paper, we address
these difficulties by: (1) converting the multiplicative model into an additive
one by taking logarithms, as proposed by some other authors; (2) using variable
splitting to obtain an equivalent constrained problem; and (3) dealing with
this optimization problem using the augmented Lagrangian framework. A set of
experiments shows that the proposed method, which we name MIDAL (multiplicative
image denoising by augmented Lagrangian), yields state-of-the-art results both
in terms of speed and denoising performance.Comment: 11 pages, 7 figures, 2 tables. To appear in the IEEE Transactions on
Image Processing
Desinvestimento industrial e as regiões portuguesas. Reflexos da mudança no espaço económico internacional
INDUSTRIAL DIVESTMENT AND PORTUGUESE REGIONS WITHIN THE CHANGES IN THE INTERNATIONAL ECONOMIC SPACE. The spatial impacts of capital mobility, especially foreign capital, are becoming increasingly complex and are extent, divestment is, in essence, another strategic option of firms and it may not be necessarily negative for regions. Still, the impacts are not identical to investment. In economic analysis, divestment in certain activities is seen as necessary to achieve regional economic restructuring. However, the time gap between the creation and destruction of activities frequently causes social and economic problems in regions. Starting with a conceptual framework of divestment, we then analyse the recent evolution of industrial employment and product in order to provide a macro-economic framework for the analysis of employment creation and destruction flows that follows. This analysis has a sectorial and regional perspective aimed at identifying different paths by regions. Finally, specific cases of foreign divestment, which have recently occurred in Portugal, are discussed, illustrating not only a micro-economic perspective of divestment but also the changes in the global value chains that point to a (re)positioning of the country in the international division of labour
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