2,964 research outputs found
Performance of Linear Field Reconstruction Techniques with Noise and Uncertain Sensor Locations
We consider a wireless sensor network, sampling a bandlimited field,
described by a limited number of harmonics. Sensor nodes are irregularly
deployed over the area of interest or subject to random motion; in addition
sensors measurements are affected by noise. Our goal is to obtain a high
quality reconstruction of the field, with the mean square error (MSE) of the
estimate as performance metric. In particular, we analytically derive the
performance of several reconstruction/estimation techniques based on linear
filtering. For each technique, we obtain the MSE, as well as its asymptotic
expression in the case where the field number of harmonics and the number of
sensors grow to infinity, while their ratio is kept constant. Through numerical
simulations, we show the validity of the asymptotic analysis, even for a small
number of sensors. We provide some novel guidelines for the design of sensor
networks when many parameters, such as field bandwidth, number of sensors,
reconstruction quality, sensor motion characteristics, and noise level of the
measures, have to be traded off
Numerical Analysis of the Non-uniform Sampling Problem
We give an overview of recent developments in the problem of reconstructing a
band-limited signal from non-uniform sampling from a numerical analysis view
point. It is shown that the appropriate design of the finite-dimensional model
plays a key role in the numerical solution of the non-uniform sampling problem.
In the one approach (often proposed in the literature) the finite-dimensional
model leads to an ill-posed problem even in very simple situations. The other
approach that we consider leads to a well-posed problem that preserves
important structural properties of the original infinite-dimensional problem
and gives rise to efficient numerical algorithms. Furthermore a fast multilevel
algorithm is presented that can reconstruct signals of unknown bandwidth from
noisy non-uniformly spaced samples. We also discuss the design of efficient
regularization methods for ill-conditioned reconstruction problems. Numerical
examples from spectroscopy and exploration geophysics demonstrate the
performance of the proposed methods
On the Estimation of Nonrandom Signal Coefficients from Jittered Samples
This paper examines the problem of estimating the parameters of a bandlimited
signal from samples corrupted by random jitter (timing noise) and additive iid
Gaussian noise, where the signal lies in the span of a finite basis. For the
presented classical estimation problem, the Cramer-Rao lower bound (CRB) is
computed, and an Expectation-Maximization (EM) algorithm approximating the
maximum likelihood (ML) estimator is developed. Simulations are performed to
study the convergence properties of the EM algorithm and compare the
performance both against the CRB and a basic linear estimator. These
simulations demonstrate that by post-processing the jittered samples with the
proposed EM algorithm, greater jitter can be tolerated, potentially reducing
on-chip ADC power consumption substantially.Comment: 11 pages, 8 figure
A recurrent neural network for classification of unevenly sampled variable stars
Astronomical surveys of celestial sources produce streams of noisy time
series measuring flux versus time ("light curves"). Unlike in many other
physical domains, however, large (and source-specific) temporal gaps in data
arise naturally due to intranight cadence choices as well as diurnal and
seasonal constraints. With nightly observations of millions of variable stars
and transients from upcoming surveys, efficient and accurate discovery and
classification techniques on noisy, irregularly sampled data must be employed
with minimal human-in-the-loop involvement. Machine learning for inference
tasks on such data traditionally requires the laborious hand-coding of
domain-specific numerical summaries of raw data ("features"). Here we present a
novel unsupervised autoencoding recurrent neural network (RNN) that makes
explicit use of sampling times and known heteroskedastic noise properties. When
trained on optical variable star catalogs, this network produces supervised
classification models that rival other best-in-class approaches. We find that
autoencoded features learned on one time-domain survey perform nearly as well
when applied to another survey. These networks can continue to learn from new
unlabeled observations and may be used in other unsupervised tasks such as
forecasting and anomaly detection.Comment: 23 pages, 14 figures. The published version is at Nature Astronomy
(https://www.nature.com/articles/s41550-017-0321-z). Source code for models,
experiments, and figures at
https://github.com/bnaul/IrregularTimeSeriesAutoencoderPaper (Zenodo Code
DOI: 10.5281/zenodo.1045560
Image reconstruction/synthesis from nonuniform data and zero/threshold crossings
We address the problem of reconstructing functions from their nonuniform data and zero/threshold crossings. We introduce a deterministic process via the Gram-Schmidt orthonormalization procedure to reconstruct functions from their nonuniform data and zero/threshold crossings. This is achieved by first introducing the nonorthogonal basis functions in a chosen 2-D domain (e.g., for a band-limited signal, a possible choice is the 2-D Fourier domain of the image) that span the signal subspace of the nonuniform data. We then use the Gram-Schmidt procedure to construct a set of orthogonal basis functions that span the linear signal subspace defined by the nonorthogonal basis functions. Next, we project the N-dimensional measurement vector (N is the number of nonuniform data or threshold crossings) onto the newly constructed orthogonal basis functions. Finally, the function at any point can be reconstructed by projecting the representation with respect to the newly constructed orthonormal basis functions onto the reconstruction basis functions that span the signal subspace of the evenly spaced sampled data. The reconstructed signal gives the minimum mean square error estimate of the original signal. This procedure gives error-free reconstruction provided that the nonorthogonal basis functions that span the signal subspace of the nonuniform data form a complete set in the signal subspace of the original band-limited signal. We apply this algorithm
to reconstruct functions from their unevenly spaced sampled data and zero crossings and also apply it to solve the problem of synthesis of a 2-D band-limited function with the prescribed level crossings
Hierarchical Bayesian sparse image reconstruction with application to MRFM
This paper presents a hierarchical Bayesian model to reconstruct sparse
images when the observations are obtained from linear transformations and
corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is
well suited to such naturally sparse image applications as it seamlessly
accounts for properties such as sparsity and positivity of the image via
appropriate Bayes priors. We propose a prior that is based on a weighted
mixture of a positive exponential distribution and a mass at zero. The prior
has hyperparameters that are tuned automatically by marginalization over the
hierarchical Bayesian model. To overcome the complexity of the posterior
distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be
used to estimate the image to be recovered, e.g. by maximizing the estimated
posterior distribution. In our fully Bayesian approach the posteriors of all
the parameters are available. Thus our algorithm provides more information than
other previously proposed sparse reconstruction methods that only give a point
estimate. The performance of our hierarchical Bayesian sparse reconstruction
method is illustrated on synthetic and real data collected from a tobacco virus
sample using a prototype MRFM instrument.Comment: v2: final version; IEEE Trans. Image Processing, 200
- âŠ