612 research outputs found
PCT, spin and statistics, and analytic wave front set
A new, more general derivation of the spin-statistics and PCT theorems is
presented. It uses the notion of the analytic wave front set of
(ultra)distributions and, in contrast to the usual approach, covers nonlocal
quantum fields. The fields are defined as generalized functions with test
functions of compact support in momentum space. The vacuum expectation values
are thereby admitted to be arbitrarily singular in their space-time dependence.
The local commutativity condition is replaced by an asymptotic commutativity
condition, which develops generalizations of the microcausality axiom
previously proposed.Comment: LaTeX, 23 pages, no figures. This version is identical to the
original published paper, but with corrected typos and slight improvements in
the exposition. The proof of Theorem 5 stated in the paper has been published
in J. Math. Phys. 45 (2004) 1944-195
Universal Denoising Networks : A Novel CNN Architecture for Image Denoising
We design a novel network architecture for learning discriminative image
models that are employed to efficiently tackle the problem of grayscale and
color image denoising. Based on the proposed architecture, we introduce two
different variants. The first network involves convolutional layers as a core
component, while the second one relies instead on non-local filtering layers
and thus it is able to exploit the inherent non-local self-similarity property
of natural images. As opposed to most of the existing deep network approaches,
which require the training of a specific model for each considered noise level,
the proposed models are able to handle a wide range of noise levels using a
single set of learned parameters, while they are very robust when the noise
degrading the latent image does not match the statistics of the noise used
during training. The latter argument is supported by results that we report on
publicly available images corrupted by unknown noise and which we compare
against solutions obtained by competing methods. At the same time the
introduced networks achieve excellent results under additive white Gaussian
noise (AWGN), which are comparable to those of the current state-of-the-art
network, while they depend on a more shallow architecture with the number of
trained parameters being one order of magnitude smaller. These properties make
the proposed networks ideal candidates to serve as sub-solvers on restoration
methods that deal with general inverse imaging problems such as deblurring,
demosaicking, superresolution, etc.Comment: Camera ready paper to appear in the Proceedings of CVPR 201
Structure tensor total variation
This is the final version of the article. Available from Society for Industrial and Applied Mathematics via the DOI in this record.We introduce a novel generic energy functional that we employ to solve inverse imaging problems
within a variational framework. The proposed regularization family, termed as structure tensor
total variation (STV), penalizes the eigenvalues of the structure tensor and is suitable for both
grayscale and vector-valued images. It generalizes several existing variational penalties, including
the total variation seminorm and vectorial extensions of it. Meanwhile, thanks to the structure
tensor’s ability to capture first-order information around a local neighborhood, the STV functionals
can provide more robust measures of image variation. Further, we prove that the STV regularizers
are convex while they also satisfy several invariance properties w.r.t. image transformations. These
properties qualify them as ideal candidates for imaging applications. In addition, for the discrete
version of the STV functionals we derive an equivalent definition that is based on the patch-based
Jacobian operator, a novel linear operator which extends the Jacobian matrix. This alternative
definition allow us to derive a dual problem formulation. The duality of the problem paves the
way for employing robust tools from convex optimization and enables us to design an efficient
and parallelizable optimization algorithm. Finally, we present extensive experiments on various
inverse imaging problems, where we compare our regularizers with other competing regularization
approaches. Our results are shown to be systematically superior, both quantitatively and visually
Quantization of the Nonlinear Sigma Model Revisited
We revisit the subject of perturbatively quantizing the nonlinear sigma model
in two dimensions from a rigorous, mathematical point of view. Our main
contribution is to make precise the cohomological problem of eliminating
potential anomalies that may arise when trying to preserve symmetries under
quantization. The symmetries we consider are twofold: (i) diffeomorphism
covariance for a general target manifold; (ii) a transitive group of isometries
when the target manifold is a homogeneous space. We show that there are no
anomalies in case (i) and that (ii) is also anomaly-free under additional
assumptions on the target homogeneous space, in agreement with the work of
Friedan. We carry out some explicit computations for the -model. Finally,
we show how a suitable notion of the renormalization group establishes the
Ricci flow as the one loop renormalization group flow of the nonlinear sigma
model.Comment: 51 page
Nonlocal Yang-Mills
We present a very simple and explicit procedure for nonlocalizing the action
of any theory which can be formulated perturbatively. When the resulting
nonlocal field theory is quantized using the functional formalism --- with unit
measure factor --- its Green's functions are finite to all orders. The
construction also ensures perturbative unitarity to all orders for scalars with
nonderivative interactions, however, decoupling is lost at one loop when vector
and tensor quanta are present. Decoupling can be restored (again, to all
orders) if a suitable measure factor exists. We compute the required measure
factor for pure Yang-Mills at order and then use it to evaluate the
vacuum polarization at one loop. A peculiar feature of our regularization
scheme is that the on-shell tree amplitudes are completely unaffected. This
implies that the nonlocal field theory can be viewed as a highly noncanonical
quantization of the original, local field equations.Comment: 38 pages, figures available upon request. No macro neede
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