3,935 research outputs found
A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems
Non-Local Total Variation (NLTV) has emerged as a useful tool in variational
methods for image recovery problems. In this paper, we extend the NLTV-based
regularization to multicomponent images by taking advantage of the Structure
Tensor (ST) resulting from the gradient of a multicomponent image. The proposed
approach allows us to penalize the non-local variations, jointly for the
different components, through various matrix norms with .
To facilitate the choice of the hyper-parameters, we adopt a constrained convex
optimization approach in which we minimize the data fidelity term subject to a
constraint involving the ST-NLTV regularization. The resulting convex
optimization problem is solved with a novel epigraphical projection method.
This formulation can be efficiently implemented thanks to the flexibility
offered by recent primal-dual proximal algorithms. Experiments are carried out
for multispectral and hyperspectral images. The results demonstrate the
interest of introducing a non-local structure tensor regularization and show
that the proposed approach leads to significant improvements in terms of
convergence speed over current state-of-the-art methods
Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition
Hyperspectral images (HSIs) are often corrupted by a mixture of several types
of noise during the acquisition process, e.g., Gaussian noise, impulse noise,
dead lines, stripes, and many others. Such complex noise could degrade the
quality of the acquired HSIs, limiting the precision of the subsequent
processing. In this paper, we present a novel tensor-based HSI restoration
approach by fully identifying the intrinsic structures of the clean HSI part
and the mixed noise part respectively. Specifically, for the clean HSI part, we
use tensor Tucker decomposition to describe the global correlation among all
bands, and an anisotropic spatial-spectral total variation (SSTV)
regularization to characterize the piecewise smooth structure in both spatial
and spectral domains. For the mixed noise part, we adopt the norm
regularization to detect the sparse noise, including stripes, impulse noise,
and dead pixels. Despite that TV regulariztion has the ability of removing
Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian
noise for some real-world scenarios. Then, we develop an efficient algorithm
for solving the resulting optimization problem by using the augmented Lagrange
multiplier (ALM) method. Finally, extensive experiments on simulated and
real-world noise HSIs are carried out to demonstrate the superiority of the
proposed method over the existing state-of-the-art ones.Comment: 15 pages, 20 figure
Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements
Background subtraction has been a fundamental and widely studied task in
video analysis, with a wide range of applications in video surveillance,
teleconferencing and 3D modeling. Recently, motivated by compressive imaging,
background subtraction from compressive measurements (BSCM) is becoming an
active research task in video surveillance. In this paper, we propose a novel
tensor-based robust PCA (TenRPCA) approach for BSCM by decomposing video frames
into backgrounds with spatial-temporal correlations and foregrounds with
spatio-temporal continuity in a tensor framework. In this approach, we use 3D
total variation (TV) to enhance the spatio-temporal continuity of foregrounds,
and Tucker decomposition to model the spatio-temporal correlations of video
background. Based on this idea, we design a basic tensor RPCA model over the
video frames, dubbed as the holistic TenRPCA model (H-TenRPCA). To characterize
the correlations among the groups of similar 3D patches of video background, we
further design a patch-group-based tensor RPCA model (PG-TenRPCA) by joint
tensor Tucker decompositions of 3D patch groups for modeling the video
background. Efficient algorithms using alternating direction method of
multipliers (ADMM) are developed to solve the proposed models. Extensive
experiments on simulated and real-world videos demonstrate the superiority of
the proposed approaches over the existing state-of-the-art approaches.Comment: To appear in IEEE TI
Closed Form Effective Conformal Anomaly Actions in D4
I present, in any D4, closed-form type B conformal anomaly effective
actions incorporating the logarithmic scaling cutoff dependence that generates
these anomalies. Their construction is based on a novel class of Weyl-invariant
tensor operators. The only known type A actions in D4 are extensions of
the Polyakov integral in D=2; despite contrary appearances, we show that their
nonlocality does not conflict with general anomaly requirements. They are,
however, physically unsatisfactory, prompting a brief attempt at better
versions.Comment: 8 pages. Improved discussion of type A actions. Some references adde
Exact solutions and spacetime singularities in nonlocal gravity
We give here a list of exact classical solutions of a large class of weakly
nonlocal theories of gravity, which are unitary and super-renormalizable (or
finite) at quantum level. It is explicitly shown that flat and Ricci-flat
spacetimes as well as maximally symmetric manifolds are exact solutions of the
equation of motion. Therefore, well-known physical spacetimes like
Schwarzschild, Kerr, (Anti-) de Sitter serve as solutions for standard matter
content. In dimension higher than four we can also have Anti-de Sitter
solutions in the presence of positive cosmological constant. We pedagogically
show how to obtain these exact solutions. Furthermore, for another version of
the theory, written in the Weyl basis, Friedmann-Robertson-Walker (FRW)
spacetimes are also exact solutions, when the matter content is given by
conformal matter (radiation). We also comment on the presence of singularities
and possible resolution of them in finite and conformally invariant theories.
"Delocalization" is proposed as a way to solve the black hole singularity
problem. In order to solve the problem of cosmological singularities it seems
crucial to have a conformally invariant or asymptotically free quantum
gravitational theory.Comment: 33 page
Trace Anomaly, Massless Scalars and the Gravitational Coupling of QCD
The anomalous effective action describing the coupling of gravity to a
non-abelian gauge theory can be determined by a variational solution of the
anomaly equation, as shown by Riegert long ago. It is given by a nonlocal
expression, with the nonlocal interaction determined by the Green's function of
a conformally covariant operator of fourth order. In recent works it has been
shown that this interaction is mediated by a simple pole in an expansion around
a Minkowski background, coupled in the infrared in the massless fermion limit.
This result relies on the local formulation of the original action in terms of
two auxiliary fields, one physical scalar and one ghost, which take the role of
massless composite degrees of freedom. In the gravity case, the two scalars
have provided ground in favour of some recent proposals of an infrared approach
to the solution of the dark energy problem, entirely based on the behaviour of
the vacuum energy at the QCD phase transition. As a test of this general
result, we perform a complete one-loop computation of the effective action
describing the coupling of a non-abelian gauge theory to gravity. We confirm
the appearance of an anomaly pole which contributes to the trace part of the
correlator and of extra poles in its trace-free part, in the quark and
gluon sectors, describing the coupling of the energy momentum tensor () to
two non abelian gauge currents ().Comment: 25 pages, 9 figures. Revised final version, to be published on Phys.
Rev.
- …