176,091 research outputs found
Structured sampling and fast reconstruction of smooth graph signals
This work concerns sampling of smooth signals on arbitrary graphs. We first
study a structured sampling strategy for such smooth graph signals that
consists of a random selection of few pre-defined groups of nodes. The number
of groups to sample to stably embed the set of -bandlimited signals is
driven by a quantity called the \emph{group} graph cumulative coherence. For
some optimised sampling distributions, we show that sampling
groups is always sufficient to stably embed the set of -bandlimited signals
but that this number can be smaller -- down to -- depending on the
structure of the groups of nodes. Fast methods to approximate these sampling
distributions are detailed. Second, we consider -bandlimited signals that
are nearly piecewise constant over pre-defined groups of nodes. We show that it
is possible to speed up the reconstruction of such signals by reducing
drastically the dimension of the vectors to reconstruct. When combined with the
proposed structured sampling procedure, we prove that the method provides
stable and accurate reconstruction of the original signal. Finally, we present
numerical experiments that illustrate our theoretical results and, as an
example, show how to combine these methods for interactive object segmentation
in an image using superpixels
The Network Nullspace Property for Compressed Sensing of Big Data over Networks
We present a novel condition, which we term the net- work nullspace property,
which ensures accurate recovery of graph signals representing massive
network-structured datasets from few signal values. The network nullspace
property couples the cluster structure of the underlying network-structure with
the geometry of the sampling set. Our results can be used to design efficient
sampling strategies based on the network topology
Implications for compressed sensing of a new sampling theorem on the sphere
A sampling theorem on the sphere has been developed recently, requiring half
as many samples as alternative equiangular sampling theorems on the sphere. A
reduction by a factor of two in the number of samples required to represent a
band-limited signal on the sphere exactly has important implications for
compressed sensing, both in terms of the dimensionality and sparsity of
signals. We illustrate the impact of this property with an inpainting problem
on the sphere, where we show the superior reconstruction performance when
adopting the new sampling theorem compared to the alternative.Comment: 1 page, 2 figures, Signal Processing with Adaptive Sparse Structured
Representations (SPARS) 201
Sparse Sampling for Inverse Problems with Tensors
We consider the problem of designing sparse sampling strategies for
multidomain signals, which can be represented using tensors that admit a known
multilinear decomposition. We leverage the multidomain structure of tensor
signals and propose to acquire samples using a Kronecker-structured sensing
function, thereby circumventing the curse of dimensionality. For designing such
sensing functions, we develop low-complexity greedy algorithms based on
submodular optimization methods to compute near-optimal sampling sets. We
present several numerical examples, ranging from multi-antenna communications
to graph signal processing, to validate the developed theory.Comment: 13 pages, 7 figure
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Deconvolution Problems for Structured Sparse Signal
This dissertation studies deconvolution problems of how structured sparse signals appear in nature, science and engineering. We discuss about the intrinsic solution to the problem of short-and-sparse deconvolution, how these solutions structured the optimization problem, and how do we design an efficient and practical algorithm base on aforementioned analytical findings. To fully utilized the information of structured sparse signals efficiently, we also propose a sensing method while the sampling acquisition is expansive, and study its sample limit and algorithms for signal recovery with limited samples
Reliable recovery of hierarchically sparse signals for Gaussian and Kronecker product measurements
We propose and analyze a solution to the problem of recovering a block sparse
signal with sparse blocks from linear measurements. Such problems naturally
emerge inter alia in the context of mobile communication, in order to meet the
scalability and low complexity requirements of massive antenna systems and
massive machine-type communication. We introduce a new variant of the Hard
Thresholding Pursuit (HTP) algorithm referred to as HiHTP. We provide both a
proof of convergence and a recovery guarantee for noisy Gaussian measurements
that exhibit an improved asymptotic scaling in terms of the sampling complexity
in comparison with the usual HTP algorithm. Furthermore, hierarchically sparse
signals and Kronecker product structured measurements naturally arise together
in a variety of applications. We establish the efficient reconstruction of
hierarchically sparse signals from Kronecker product measurements using the
HiHTP algorithm. Additionally, we provide analytical results that connect our
recovery conditions to generalized coherence measures. Again, our recovery
results exhibit substantial improvement in the asymptotic sampling complexity
scaling over the standard setting. Finally, we validate in numerical
experiments that for hierarchically sparse signals, HiHTP performs
significantly better compared to HTP.Comment: 11+4 pages, 5 figures. V3: Incomplete funding information corrected
and minor typos corrected. V4: Change of title and additional author Axel
Flinth. Included new results on Kronecker product measurements and relations
of HiRIP to hierarchical coherence measures. Improved presentation of general
hierarchically sparse signals and correction of minor typo
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