10,043 research outputs found
Discrete Signal Processing on Graphs: Frequency Analysis
Signals and datasets that arise in physical and engineering applications, as
well as social, genetics, biomolecular, and many other domains, are becoming
increasingly larger and more complex. In contrast to traditional time and image
signals, data in these domains are supported by arbitrary graphs. Signal
processing on graphs extends concepts and techniques from traditional signal
processing to data indexed by generic graphs. This paper studies the concepts
of low and high frequencies on graphs, and low-, high-, and band-pass graph
filters. In traditional signal processing, there concepts are easily defined
because of a natural frequency ordering that has a physical interpretation. For
signals residing on graphs, in general, there is no obvious frequency ordering.
We propose a definition of total variation for graph signals that naturally
leads to a frequency ordering on graphs and defines low-, high-, and band-pass
graph signals and filters. We study the design of graph filters with specified
frequency response, and illustrate our approach with applications to sensor
malfunction detection and data classification
Type II and heterotic one loop string effective actions in four dimensions
We analyze the reduction to four dimensions of the R^4 terms which are part
of the ten-dimensional string effective actions, both at tree level and one
loop. We show that there are two independent combinations of R^4 present, at
one loop, in the type IIA four dimensional effective action, which means they
both have their origin in M-theory. The d=4 heterotic effective action also has
such terms. This contradicts the common belief thathere is only one R^4 term in
four-dimensional supergravity theories, given by the square of the Bel-Robinson
tensor. In pure N=1 supergravity this new R^4 combination cannot be directly
supersymmetrized, but we show that, when coupled to a scalar chiral multiplet
(violating the U(1) -symmetry), it emerges in the action after elimination
of the auxiliary fields.Comment: v2: 22 pages. Discussion on the new R^4 term and extended
supergravity has been abridged and improved. Published versio
Convergence Rate Analysis of Distributed Gossip (Linear Parameter) Estimation: Fundamental Limits and Tradeoffs
The paper considers gossip distributed estimation of a (static) distributed
random field (a.k.a., large scale unknown parameter vector) observed by
sparsely interconnected sensors, each of which only observes a small fraction
of the field. We consider linear distributed estimators whose structure
combines the information \emph{flow} among sensors (the \emph{consensus} term
resulting from the local gossiping exchange among sensors when they are able to
communicate) and the information \emph{gathering} measured by the sensors (the
\emph{sensing} or \emph{innovations} term.) This leads to mixed time scale
algorithms--one time scale associated with the consensus and the other with the
innovations. The paper establishes a distributed observability condition
(global observability plus mean connectedness) under which the distributed
estimates are consistent and asymptotically normal. We introduce the
distributed notion equivalent to the (centralized) Fisher information rate,
which is a bound on the mean square error reduction rate of any distributed
estimator; we show that under the appropriate modeling and structural network
communication conditions (gossip protocol) the distributed gossip estimator
attains this distributed Fisher information rate, asymptotically achieving the
performance of the optimal centralized estimator. Finally, we study the
behavior of the distributed gossip estimator when the measurements fade (noise
variance grows) with time; in particular, we consider the maximum rate at which
the noise variance can grow and still the distributed estimator being
consistent, by showing that, as long as the centralized estimator is
consistent, the distributed estimator remains consistent.Comment: Submitted for publication, 30 page
Consensus State Gram Matrix Estimation for Stochastic Switching Networks from Spectral Distribution Moments
Reaching distributed average consensus quickly and accurately over a network
through iterative dynamics represents an important task in numerous distributed
applications. Suitably designed filters applied to the state values can
significantly improve the convergence rate. For constant networks, these
filters can be viewed in terms of graph signal processing as polynomials in a
single matrix, the consensus iteration matrix, with filter response evaluated
at its eigenvalues. For random, time-varying networks, filter design becomes
more complicated, involving eigendecompositions of sums and products of random,
time-varying iteration matrices. This paper focuses on deriving an estimate for
the Gram matrix of error in the state vectors over a filtering window for
large-scale, stationary, switching random networks. The result depends on the
moments of the empirical spectral distribution, which can be estimated through
Monte-Carlo simulation. This work then defines a quadratic objective function
to minimize the expected consensus estimate error norm. Simulation results
provide support for the approximation.Comment: 52nd Asilomar Conference on Signals, Systems, and Computers (Asilomar
2017
Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields
We present \emph{telescoping} recursive representations for both continuous
and discrete indexed noncausal Gauss-Markov random fields. Our recursions start
at the boundary (a hypersurface in , ) and telescope inwards.
For example, for images, the telescoping representation reduce recursions from
to , i.e., to recursions on a single dimension. Under
appropriate conditions, the recursions for the random field are linear
stochastic differential/difference equations driven by white noise, for which
we derive recursive estimation algorithms, that extend standard algorithms,
like the Kalman-Bucy filter and the Rauch-Tung-Striebel smoother, to noncausal
Markov random fields.Comment: To appear in the Transactions on Information Theor
Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for DCTs and DSTs
This paper presents a systematic methodology based on the algebraic theory of
signal processing to classify and derive fast algorithms for linear transforms.
Instead of manipulating the entries of transform matrices, our approach derives
the algorithms by stepwise decomposition of the associated signal models, or
polynomial algebras. This decomposition is based on two generic methods or
algebraic principles that generalize the well-known Cooley-Tukey FFT and make
the algorithms' derivations concise and transparent. Application to the 16
discrete cosine and sine transforms yields a large class of fast algorithms,
many of which have not been found before.Comment: 31 pages, more information at http://www.ece.cmu.edu/~smar
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