19,292 research outputs found
Shape optimization for quadratic functionals and states with random right-hand sides
In this work, we investigate a particular class of shape optimization
problems under uncertainties on the input parameters. More precisely, we are
interested in the minimization of the expectation of a quadratic objective in a
situation where the state function depends linearly on a random input
parameter. This framework covers important objectives such as tracking-type
functionals for elliptic second order partial differential equations and the
compliance in linear elasticity. We show that the robust objective and its
gradient are completely and explicitly determined by low-order moments of the
random input. We then derive a cheap, deterministic algorithm to minimize this
objective and present model cases in structural optimization
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
Depth Superresolution using Motion Adaptive Regularization
Spatial resolution of depth sensors is often significantly lower compared to
that of conventional optical cameras. Recent work has explored the idea of
improving the resolution of depth using higher resolution intensity as a side
information. In this paper, we demonstrate that further incorporating temporal
information in videos can significantly improve the results. In particular, we
propose a novel approach that improves depth resolution, exploiting the
space-time redundancy in the depth and intensity using motion-adaptive low-rank
regularization. Experiments confirm that the proposed approach substantially
improves the quality of the estimated high-resolution depth. Our approach can
be a first component in systems using vision techniques that rely on high
resolution depth information
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