609,717 research outputs found
Total Generalized Variation for Manifold-valued Data
In this paper we introduce the notion of second-order total generalized
variation (TGV) regularization for manifold-valued data in a discrete setting.
We provide an axiomatic approach to formalize reasonable generalizations of TGV
to the manifold setting and present two possible concrete instances that
fulfill the proposed axioms. We provide well-posedness results and present
algorithms for a numerical realization of these generalizations to the manifold
setup. Further, we provide experimental results for synthetic and real data to
further underpin the proposed generalization numerically and show its potential
for applications with manifold-valued data
Iterative algorithms for total variation-like reconstructions in seismic tomography
A qualitative comparison of total variation like penalties (total variation,
Huber variant of total variation, total generalized variation, ...) is made in
the context of global seismic tomography. Both penalized and constrained
formulations of seismic recovery problems are treated. A number of simple
iterative recovery algorithms applicable to these problems are described. The
convergence speed of these algorithms is compared numerically in this setting.
For the constrained formulation a new algorithm is proposed and its convergence
is proven.Comment: 28 pages, 8 figures. Corrected sign errors in formula (25
Post-Reconstruction Deconvolution of PET Images by Total Generalized Variation Regularization
Improving the quality of positron emission tomography (PET) images, affected
by low resolution and high level of noise, is a challenging task in nuclear
medicine and radiotherapy. This work proposes a restoration method, achieved
after tomographic reconstruction of the images and targeting clinical
situations where raw data are often not accessible. Based on inverse problem
methods, our contribution introduces the recently developed total generalized
variation (TGV) norm to regularize PET image deconvolution. Moreover, we
stabilize this procedure with additional image constraints such as positivity
and photometry invariance. A criterion for updating and adjusting automatically
the regularization parameter in case of Poisson noise is also presented.
Experiments are conducted on both synthetic data and real patient images.Comment: First published in the Proceedings of the 23rd European Signal
Processing Conference (EUSIPCO-2015) in 2015, published by EURASI
Strain Analysis by a Total Generalized Variation Regularized Optical Flow Model
In this paper we deal with the important problem of estimating the local
strain tensor from a sequence of micro-structural images realized during
deformation tests of engineering materials. Since the strain tensor is defined
via the Jacobian of the displacement field, we propose to compute the
displacement field by a variational model which takes care of properties of the
Jacobian of the displacement field. In particular we are interested in areas of
high strain. The data term of our variational model relies on the brightness
invariance property of the image sequence. As prior we choose the second order
total generalized variation of the displacement field. This prior splits the
Jacobian of the displacement field into a smooth and a non-smooth part. The
latter reflects the material cracks. An additional constraint is incorporated
to handle physical properties of the non-smooth part for tensile tests. We
prove that the resulting convex model has a minimizer and show how a
primal-dual method can be applied to find a minimizer. The corresponding
algorithm has the advantage that the strain tensor is directly computed within
the iteration process. Our algorithm is further equipped with a coarse-to-fine
strategy to cope with larger displacements. Numerical examples with simulated
and experimental data demonstrate the very good performance of our algorithm.
In comparison to state-of-the-art engineering software for strain analysis our
method can resolve local phenomena much better
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