29,558 research outputs found
Tracking Time-Vertex Propagation using Dynamic Graph Wavelets
Graph Signal Processing generalizes classical signal processing to signal or
data indexed by the vertices of a weighted graph. So far, the research efforts
have been focused on static graph signals. However numerous applications
involve graph signals evolving in time, such as spreading or propagation of
waves on a network. The analysis of this type of data requires a new set of
methods that fully takes into account the time and graph dimensions. We propose
a novel class of wavelet frames named Dynamic Graph Wavelets, whose time-vertex
evolution follows a dynamic process. We demonstrate that this set of functions
can be combined with sparsity based approaches such as compressive sensing to
reveal information on the dynamic processes occurring on a graph. Experiments
on real seismological data show the efficiency of the technique, allowing to
estimate the epicenter of earthquake events recorded by a seismic network
Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing
In this work the dynamic compressive sensing (CS) problem of recovering
sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear
measurements is explored from a Bayesian perspective. While there has been a
handful of previously proposed Bayesian dynamic CS algorithms in the
literature, the ability to perform inference on high-dimensional problems in a
computationally efficient manner remains elusive. In response, we propose a
probabilistic dynamic CS signal model that captures both amplitude and support
correlation structure, and describe an approximate message passing algorithm
that performs soft signal estimation and support detection with a computational
complexity that is linear in all problem dimensions. The algorithm, DCS-AMP,
can perform either causal filtering or non-causal smoothing, and is capable of
learning model parameters adaptively from the data through an
expectation-maximization learning procedure. We provide numerical evidence that
DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety
of operating conditions. We further describe the result of applying DCS-AMP to
two real dynamic CS datasets, as well as a frequency estimation task, to
bolster our claim that DCS-AMP is capable of offering state-of-the-art
performance and speed on real-world high-dimensional problems.Comment: 32 pages, 7 figure
Distributed Adaptive Learning of Graph Signals
The aim of this paper is to propose distributed strategies for adaptive
learning of signals defined over graphs. Assuming the graph signal to be
bandlimited, the method enables distributed reconstruction, with guaranteed
performance in terms of mean-square error, and tracking from a limited number
of sampled observations taken from a subset of vertices. A detailed mean square
analysis is carried out and illustrates the role played by the sampling
strategy on the performance of the proposed method. Finally, some useful
strategies for distributed selection of the sampling set are provided. Several
numerical results validate our theoretical findings, and illustrate the
performance of the proposed method for distributed adaptive learning of signals
defined over graphs.Comment: To appear in IEEE Transactions on Signal Processing, 201
Graph Signal Processing: Overview, Challenges and Applications
Research in Graph Signal Processing (GSP) aims to develop tools for
processing data defined on irregular graph domains. In this paper we first
provide an overview of core ideas in GSP and their connection to conventional
digital signal processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
Inpainting of long audio segments with similarity graphs
We present a novel method for the compensation of long duration data loss in
audio signals, in particular music. The concealment of such signal defects is
based on a graph that encodes signal structure in terms of time-persistent
spectral similarity. A suitable candidate segment for the substitution of the
lost content is proposed by an intuitive optimization scheme and smoothly
inserted into the gap, i.e. the lost or distorted signal region. Extensive
listening tests show that the proposed algorithm provides highly promising
results when applied to a variety of real-world music signals
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