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@PHDTHESIS{Koep:764234,
author = {Koep, Niklas},
othercontributors = {Mathar, Rudolf and Rauhut, Holger},
title = {{Q}uantized compressive sampling for structured signal
estimation; 1},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {Mainz},
reportid = {RWTH-2019-06704},
isbn = {978-3-95886-291-3},
pages = {1 Online-Ressource (x, 189 Seiten) : Illustrationen},
year = {2019},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University; Dissertation, RWTH Aachen University, 2019},
abstract = {This thesis investigates different approaches to enable the
use of compressed sensing (CS)-based acquisition devices in
resource-constrained environments relying on cheap,
energy-efficient sensors. We consider the acquisition of
structured low-complexity signals from excessively quantized
1-bit observations, as well as partial compressive
measurements collected by one or multiple sensors. In both
scenarios, the central goal is to alleviate the complexity
of sensing devices in order to enable signal acquisition by
simple, inexpensive sensors. In the first part of the
thesis, we address the reconstruction of signals with a
sparse Fourier transform from 1-bit time domain
measurements. We propose a modification of the binary
iterative hard thresholding algorithm, which accounts for
the conjugate symmetric structure of the underlying signal
space. In this context, a modification of the hard
thresholding operator is developed, whose use extends to
various other (quantized) CS recovery algorithms. In
addition to undersampled measurements, we also consider
oversampled signal representations, in which case the
measurement operator is deterministic rather than
constructed randomly. Numerical experiments verify the
correct behavior of the proposed methods. The remainder of
the thesis focuses on the reconstruction of group-sparse
signals, a signal class in which nonzero components are
assumed to appear in nonoverlapping coefficient groups. We
first focus on 1-bit quantized Gaussian observations and
derive theoretical guarantees for several reconstruction
schemes to recover target vectors with a desired level of
accuracy. We also address recovery based on dithered
quantized observations to resolve the scale ambiguity
inherent in the 1-bit CS model to allow for the recovery of
both direction and magnitude of group-sparse vectors. In the
last part, the acquisition of group-sparse vectors by a
collection of independent sensors, which each observe a
different portion of a target vector, is considered.
Generalizing earlier results for the canonical sparsity
model, a bound on the number of measurements required to
allow for stable and robust signal recovery is established.
The proof relies on a powerful concentration bound on the
suprema of chaos processes. In order to establish our main
result, we develop an extension of Maurey’s empirical
method to bound the covering number of sets which can be
represented as convex combinations of elements in compact
convex sets.},
cin = {613410},
ddc = {621.3},
cid = {$I:(DE-82)613410_20140620$},
typ = {PUB:(DE-HGF)11 / PUB:(DE-HGF)3},
doi = {10.18154/RWTH-2019-06704},
url = {https://publications.rwth-aachen.de/record/764234},
}
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