3,331 research outputs found
Another look at synchronized neutrino oscillations
In dense neutrino backgrounds present in supernovae and in the early Universe
neutrino oscillations may exhibit complex collective phenomena, such as
synchronized oscillations, bipolar oscillations and spectral splits and swaps.
We consider in detail possible decoherence effects on the simplest of these
phenomena -- synchronized neutrino oscillations that can occur in a uniform and
isotropic neutrino gas. We develop an exact formalism of spectral moments of
the flavour spin vectors describing such a system and then apply it to find
analytical approaches that allow one to study decoherence effects on its
late-time evolution. This turns out to be possible in part due to the existence
of the (previously unknown) exact conservation law satisfied by the quantities
describing the considered neutrino system. Interpretation of the decoherence
effects in terms of neutrino wave packet separation is also given, both in the
adiabatic and non-adiabatic regimes of neutrino flavour evolution.Comment: LaTeX, 32 pages, 3 figures. V2: minor textual changes, references and
an acknowledgement added, results and conclusions unchange
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
We address the denoising of images contaminated with multiplicative noise,
e.g. speckle noise. Classical ways to solve such problems are filtering,
statistical (Bayesian) methods, variational methods, and methods that convert
the multiplicative noise into additive noise (using a logarithmic function),
shrinkage of the coefficients of the log-image data in a wavelet basis or in a
frame, and transform back the result using an exponential function. We propose
a method composed of several stages: we use the log-image data and apply a
reasonable under-optimal hard-thresholding on its curvelet transform; then we
apply a variational method where we minimize a specialized criterion composed
of an data-fitting to the thresholded coefficients and a Total
Variation regularization (TV) term in the image domain; the restored image is
an exponential of the obtained minimizer, weighted in a way that the mean of
the original image is preserved. Our restored images combine the advantages of
shrinkage and variational methods and avoid their main drawbacks. For the
minimization stage, we propose a properly adapted fast minimization scheme
based on Douglas-Rachford splitting. The existence of a minimizer of our
specialized criterion being proven, we demonstrate the convergence of the
minimization scheme. The obtained numerical results outperform the main
alternative methods
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
We consider linear inverse problems where the solution is assumed to have a
sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that
replacing the usual quadratic regularizing penalties by weighted l^p-penalties
on the coefficients of such expansions, with 1 < or = p < or =2, still
regularizes the problem. If p < 2, regularized solutions of such l^p-penalized
problems will have sparser expansions, with respect to the basis under
consideration. To compute the corresponding regularized solutions we propose an
iterative algorithm that amounts to a Landweber iteration with thresholding (or
nonlinear shrinkage) applied at each iteration step. We prove that this
algorithm converges in norm. We also review some potential applications of this
method.Comment: 30 pages, 3 figures; this is version 2 - changes with respect to v1:
small correction in proof (but not statement of) lemma 3.15; description of
Besov spaces in intro and app A clarified (and corrected); smaller pointsize
(making 30 instead of 38 pages
Variational image restoration by means of wavelets: Simultaneous decomposition, deblurring, and denoising
AbstractInspired by papers of Vese–Osher [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and Osher–Solé–Vese [Image decomposition and restoration using total variation minimization and the H−1 norm, Technical Report 02-57, 2002] we present a wavelet-based treatment of variational problems arising in the field of image processing. In particular, we follow their approach and discuss a special class of variational functionals that induce a decomposition of images into oscillating and cartoon components and possibly an appropriate ‘noise’ component. In the setting of [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and [Image decomposition and restoration using total variation minimization and the H−1 norm, Technical Report 02-57, 2002], the cartoon component of an image is modeled by a BV function; the corresponding incorporation of BV penalty terms in the variational functional leads to PDE schemes that are numerically intensive. By replacing the BV penalty term by a B11(L1) term (which amounts to a slightly stronger constraint on the minimizer), and writing the problem in a wavelet framework, we obtain elegant and numerically efficient schemes with results very similar to those obtained in [Modeling textures with total variation minimization and oscillating patterns in image processing, Technical Report 02-19, 2002] and [Image decomposition and restoration using total variation minimization and the H−1 norm, Technical Report 02-57, 2002]. This approach allows us, moreover, to incorporate general bounded linear blur operators into the problem so that the minimization leads to a simultaneous decomposition, deblurring and denoising
Unsupervised Texture Segmentation Using Active Contour Model and Oscillating Information
Textures often occur in real-world images and may cause considerable difficulties in image segmentation. In order to segment texture images, we propose a new segmentation model that combines image decomposition model and active contour model. The former model is capable of decomposing structural and oscillating components separately from texture image, and the latter model can be used to provide smooth segmentation contour. In detail, we just replace the data term of piecewise constant/smooth approximation in CCV (convex Chan-Vese) model with that of image decomposition model-VO (Vese-Osher). Therefore, our proposed model can estimate both structural and oscillating components of texture images as well as segment textures simultaneously. In addition, we design fast Split-Bregman algorithm for our proposed model. Finally, the performance of our method is demonstrated by segmenting some synthetic and real texture images
L0 Sparse Inverse Covariance Estimation
Recently, there has been focus on penalized log-likelihood covariance
estimation for sparse inverse covariance (precision) matrices. The penalty is
responsible for inducing sparsity, and a very common choice is the convex
norm. However, the best estimator performance is not always achieved with this
penalty. The most natural sparsity promoting "norm" is the non-convex
penalty but its lack of convexity has deterred its use in sparse maximum
likelihood estimation. In this paper we consider non-convex penalized
log-likelihood inverse covariance estimation and present a novel cyclic descent
algorithm for its optimization. Convergence to a local minimizer is proved,
which is highly non-trivial, and we demonstrate via simulations the reduced
bias and superior quality of the penalty as compared to the
penalty
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