69,804 research outputs found
Compressive Source Separation: Theory and Methods for Hyperspectral Imaging
With the development of numbers of high resolution data acquisition systems
and the global requirement to lower the energy consumption, the development of
efficient sensing techniques becomes critical. Recently, Compressed Sampling
(CS) techniques, which exploit the sparsity of signals, have allowed to
reconstruct signal and images with less measurements than the traditional
Nyquist sensing approach. However, multichannel signals like Hyperspectral
images (HSI) have additional structures, like inter-channel correlations, that
are not taken into account in the classical CS scheme. In this paper we exploit
the linear mixture of sources model, that is the assumption that the
multichannel signal is composed of a linear combination of sources, each of
them having its own spectral signature, and propose new sampling schemes
exploiting this model to considerably decrease the number of measurements
needed for the acquisition and source separation. Moreover, we give theoretical
lower bounds on the number of measurements required to perform reconstruction
of both the multichannel signal and its sources. We also proposed optimization
algorithms and extensive experimentation on our target application which is
HSI, and show that our approach recovers HSI with far less measurements and
computational effort than traditional CS approaches.Comment: 32 page
Stochastic collocation on unstructured multivariate meshes
Collocation has become a standard tool for approximation of parameterized
systems in the uncertainty quantification (UQ) community. Techniques for
least-squares regularization, compressive sampling recovery, and interpolatory
reconstruction are becoming standard tools used in a variety of applications.
Selection of a collocation mesh is frequently a challenge, but methods that
construct geometrically "unstructured" collocation meshes have shown great
potential due to attractive theoretical properties and direct, simple
generation and implementation. We investigate properties of these meshes,
presenting stability and accuracy results that can be used as guides for
generating stochastic collocation grids in multiple dimensions.Comment: 29 pages, 6 figure
Fast Escape from Quantum Mazes in Integrated Photonics
Escaping from a complex maze, by exploring different paths with several
decision-making branches in order to reach the exit, has always been a very
challenging and fascinating task. Wave field and quantum objects may explore a
complex structure in parallel by interference effects, but without necessarily
leading to more efficient transport. Here, inspired by recent observations in
biological energy transport phenomena, we demonstrate how a quantum walker can
efficiently reach the output of a maze by partially suppressing the presence of
interference. In particular, we show theoretically an unprecedented improvement
in transport efficiency for increasing maze size with respect to purely quantum
and classical approaches. In addition, we investigate experimentally these
hybrid transport phenomena, by mapping the maze problem in an integrated
waveguide array, probed by coherent light, hence successfully testing our
theoretical results. These achievements may lead towards future bio-inspired
photonics technologies for more efficient transport and computation.Comment: 13 pages, 10 figure
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