21,569 research outputs found
A kepstrum approach to filtering, smoothing and prediction
The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization
where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new
approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to
adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the
type or order of the signal generating model. And unlike other approaches - with the exception of spectral
subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to
stationary signal and additive white noise
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
The adaptive patched cubature filter and its implementation
There are numerous contexts where one wishes to describe the state of a
randomly evolving system. Effective solutions combine models that quantify the
underlying uncertainty with available observational data to form scientifically
reasonable estimates for the uncertainty in the system state. Stochastic
differential equations are often used to mathematically model the underlying
system.
The Kusuoka-Lyons-Victoir (KLV) approach is a higher order particle method
for approximating the weak solution of a stochastic differential equation that
uses a weighted set of scenarios to approximate the evolving probability
distribution to a high order of accuracy. The algorithm can be performed by
integrating along a number of carefully selected bounded variation paths. The
iterated application of the KLV method has a tendency for the number of
particles to increase. This can be addressed and, together with local dynamic
recombination, which simplifies the support of discrete measure without harming
the accuracy of the approximation, the KLV method becomes eligible to solve the
filtering problem in contexts where one desires to maintain an accurate
description of the ever-evolving conditioned measure.
In addition to the alternate application of the KLV method and recombination,
we make use of the smooth nature of the likelihood function and high order
accuracy of the approximations to lead some of the particles immediately to the
next observation time and to build into the algorithm a form of automatic high
order adaptive importance sampling.Comment: to appear in Communications in Mathematical Sciences. arXiv admin
note: substantial text overlap with arXiv:1311.675
Integrated adaptive filtering and design for control experiments of flexible structures
A novel method is presented of identifying a state space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relations between the state space model and the finite difference model for linear stochastic systems derived through projection filters. It is proven that least squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model. In estimating the corresponding state estimator gain, a z-domain method is used. First the deterministic component of the output is subtracted out, and then the state estimator gain is obtained by whitening the remaining signal. Experimental example is used to illustrate the feasibility of the method
Forecasting Time Series with VARMA Recursions on Graphs
Graph-based techniques emerged as a choice to deal with the dimensionality
issues in modeling multivariate time series. However, there is yet no complete
understanding of how the underlying structure could be exploited to ease this
task. This work provides contributions in this direction by considering the
forecasting of a process evolving over a graph. We make use of the
(approximate) time-vertex stationarity assumption, i.e., timevarying graph
signals whose first and second order statistical moments are invariant over
time and correlated to a known graph topology. The latter is combined with VAR
and VARMA models to tackle the dimensionality issues present in predicting the
temporal evolution of multivariate time series. We find out that by projecting
the data to the graph spectral domain: (i) the multivariate model estimation
reduces to that of fitting a number of uncorrelated univariate ARMA models and
(ii) an optimal low-rank data representation can be exploited so as to further
reduce the estimation costs. In the case that the multivariate process can be
observed at a subset of nodes, the proposed models extend naturally to Kalman
filtering on graphs allowing for optimal tracking. Numerical experiments with
both synthetic and real data validate the proposed approach and highlight its
benefits over state-of-the-art alternatives.Comment: submitted to the IEEE Transactions on Signal Processin
A probabilistic interpretation of set-membership filtering: application to polynomial systems through polytopic bounding
Set-membership estimation is usually formulated in the context of set-valued
calculus and no probabilistic calculations are necessary. In this paper, we
show that set-membership estimation can be equivalently formulated in the
probabilistic setting by employing sets of probability measures. Inference in
set-membership estimation is thus carried out by computing expectations with
respect to the updated set of probability measures P as in the probabilistic
case. In particular, it is shown that inference can be performed by solving a
particular semi-infinite linear programming problem, which is a special case of
the truncated moment problem in which only the zero-th order moment is known
(i.e., the support). By writing the dual of the above semi-infinite linear
programming problem, it is shown that, if the nonlinearities in the measurement
and process equations are polynomial and if the bounding sets for initial
state, process and measurement noises are described by polynomial inequalities,
then an approximation of this semi-infinite linear programming problem can
efficiently be obtained by using the theory of sum-of-squares polynomial
optimization. We then derive a smart greedy procedure to compute a polytopic
outer-approximation of the true membership-set, by computing the minimum-volume
polytope that outer-bounds the set that includes all the means computed with
respect to P
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