3,830 research outputs found
Sampling and Reconstruction of Spatial Fields using Mobile Sensors
Spatial sampling is traditionally studied in a static setting where static
sensors scattered around space take measurements of the spatial field at their
locations. In this paper we study the emerging paradigm of sampling and
reconstructing spatial fields using sensors that move through space. We show
that mobile sensing offers some unique advantages over static sensing in
sensing time-invariant bandlimited spatial fields. Since a moving sensor
encounters such a spatial field along its path as a time-domain signal, a
time-domain anti-aliasing filter can be employed prior to sampling the signal
received at the sensor. Such a filtering procedure, when used by a
configuration of sensors moving at constant speeds along equispaced parallel
lines, leads to a complete suppression of spatial aliasing in the direction of
motion of the sensors. We analytically quantify the advantage of using such a
sampling scheme over a static sampling scheme by computing the reduction in
sampling noise due to the filter. We also analyze the effects of non-uniform
sensor speeds on the reconstruction accuracy. Using simulation examples we
demonstrate the advantages of mobile sampling over static sampling in practical
problems.
We extend our analysis to sampling and reconstruction schemes for monitoring
time-varying bandlimited fields using mobile sensors. We demonstrate that in
some situations we require a lower density of sensors when using a mobile
sensing scheme instead of the conventional static sensing scheme. The exact
advantage is quantified for a problem of sampling and reconstructing an audio
field.Comment: Submitted to IEEE Transactions on Signal Processing May 2012; revised
Oct 201
Network correlated data gathering with explicit communication: NP-completeness and algorithms
We consider the problem of correlated data gathering by a network with a sink node and a tree-based communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. For source coding of correlated data, we consider a joint entropy-based coding model with explicit communication where coding is simple and the transmission structure optimization is difficult. We first formulate the optimization problem definition in the general case and then we study further a network setting where the entropy conditioning at nodes does not depend on the amount of side information, but only on its availability. We prove that even in this simple case, the optimization problem is NP-hard. We propose some efficient, scalable, and distributed heuristic approximation algorithms for solving this problem and show by numerical simulations that the total transmission cost can be significantly improved over direct transmission or the shortest path tree. We also present an approximation algorithm that provides a tree transmission structure with total cost within a constant factor from the optimal
Omnidirectional Bats, Point-to-Plane Distances, and the Price of Uniqueness
We study simultaneous localization and mapping with a device that uses
reflections to measure its distance from walls. Such a device can be realized
acoustically with a synchronized collocated source and receiver; it behaves
like a bat with no capacity for directional hearing or vocalizing. In this
paper we generalize our previous work in 2D, and show that the 3D case is not
just a simple extension, but rather a fundamentally different inverse problem.
While generically the 2D problem has a unique solution, in 3D uniqueness is
always absent in rooms with fewer than nine walls. In addition to the complete
characterization of ambiguities which arise due to this non-uniqueness, we
propose a robust solution for inexact measurements similar to analogous results
for Euclidean Distance Matrices. Our theoretical results have important
consequences for the design of collocated range-only SLAM systems, and we
support them with an array of computer experiments.Comment: 5 pages, 8 figures, submitted to ICASSP 201
Shapes from Echoes: Uniqueness from Point-to-Plane Distance Matrices
We study the problem of localizing a configuration of points and planes from
the collection of point-to-plane distances. This problem models simultaneous
localization and mapping from acoustic echoes as well as the notable "structure
from sound" approach to microphone localization with unknown sources. In our
earlier work we proposed computational methods for localization from
point-to-plane distances and noted that such localization suffers from various
ambiguities beyond the usual rigid body motions; in this paper we provide a
complete characterization of uniqueness. We enumerate equivalence classes of
configurations which lead to the same distance measurements as a function of
the number of planes and points, and algebraically characterize the related
transformations in both 2D and 3D. Here we only discuss uniqueness;
computational tools and heuristics for practical localization from
point-to-plane distances using sound will be addressed in a companion paper.Comment: 13 pages, 13 figure
Look, no Beacons! Optimal All-in-One EchoSLAM
We study the problem of simultaneously reconstructing a polygonal room and a
trajectory of a device equipped with a (nearly) collocated omnidirectional
source and receiver. The device measures arrival times of echoes of pulses
emitted by the source and picked up by the receiver. No prior knowledge about
the device's trajectory is required. Most existing approaches addressing this
problem assume multiple sources or receivers, or they assume that some of these
are static, serving as beacons. Unlike earlier approaches, we take into account
the measurement noise and various constraints on the geometry by formulating
the solution as a minimizer of a cost function similar to \emph{stress} in
multidimensional scaling. We study uniqueness of the reconstruction from
first-order echoes, and we show that in addition to the usual invariance to
rigid motions, new ambiguities arise for important classes of rooms and
trajectories. We support our theoretical developments with a number of
numerical experiments.Comment: 5 pages, 6 figures, submitted to Asilomar Conference on Signals,
Systems, and Computers Websit
Bound and Conquer: Improving Triangulation by Enforcing Consistency
We study the accuracy of triangulation in multi-camera systems with respect
to the number of cameras. We show that, under certain conditions, the optimal
achievable reconstruction error decays quadratically as more cameras are added
to the system. Furthermore, we analyse the error decay-rate of major
state-of-the-art algorithms with respect to the number of cameras. To this end,
we introduce the notion of consistency for triangulation, and show that
consistent reconstruction algorithms achieve the optimal quadratic decay, which
is asymptotically faster than some other methods. Finally, we present
simulations results supporting our findings. Our simulations have been
implemented in MATLAB and the resulting code is available in the supplementary
material.Comment: 8 pages, 4 figures, Submitted to IEEE Transactions on Pattern
Analysis and Machine Intelligenc
Distributed Successive Approximation Coding using Broadcast Advantage: The Two-Encoder Case
Traditional distributed source coding rarely considers the possible link
between separate encoders. However, the broadcast nature of wireless
communication in sensor networks provides a free gossip mechanism which can be
used to simplify encoding/decoding and reduce transmission power. Using this
broadcast advantage, we present a new two-encoder scheme which imitates the
ping-pong game and has a successive approximation structure. For the quadratic
Gaussian case, we prove that this scheme is successively refinable on the
{sum-rate, distortion pair} surface, which is characterized by the
rate-distortion region of the distributed two-encoder source coding. A
potential energy saving over conventional distributed coding is also
illustrated. This ping-pong distributed coding idea can be extended to the
multiple encoder case and provides the theoretical foundation for a new class
of distributed image coding method in wireless scenarios.Comment: In Proceedings of the 48th Annual Allerton Conference on
Communication, Control and Computing, University of Illinois, Monticello, IL,
September 29 - October 1, 201
Raking the Cocktail Party
We present the concept of an acoustic rake receiver---a microphone beamformer
that uses echoes to improve the noise and interference suppression. The rake
idea is well-known in wireless communications; it involves constructively
combining different multipath components that arrive at the receiver antennas.
Unlike spread-spectrum signals used in wireless communications, speech signals
are not orthogonal to their shifts. Therefore, we focus on the spatial
structure, rather than temporal. Instead of explicitly estimating the channel,
we create correspondences between early echoes in time and image sources in
space. These multiple sources of the desired and the interfering signal offer
additional spatial diversity that we can exploit in the beamformer design.
We present several "intuitive" and optimal formulations of acoustic rake
receivers, and show theoretically and numerically that the rake formulation of
the maximum signal-to-interference-and-noise beamformer offers significant
performance boosts in terms of noise and interference suppression. Beyond
signal-to-noise ratio, we observe gains in terms of the \emph{perceptual
evaluation of speech quality} (PESQ) metric for the speech quality. We
accompany the paper by the complete simulation and processing chain written in
Python. The code and the sound samples are available online at
\url{http://lcav.github.io/AcousticRakeReceiver/}.Comment: 12 pages, 11 figures, Accepted for publication in IEEE Journal on
Selected Topics in Signal Processing (Special Issue on Spatial Audio
On the Information Rates of the Plenoptic Function
The {\it plenoptic function} (Adelson and Bergen, 91) describes the visual
information available to an observer at any point in space and time. Samples of
the plenoptic function (POF) are seen in video and in general visual content,
and represent large amounts of information. In this paper we propose a
stochastic model to study the compression limits of the plenoptic function. In
the proposed framework, we isolate the two fundamental sources of information
in the POF: the one representing the camera motion and the other representing
the information complexity of the "reality" being acquired and transmitted. The
sources of information are combined, generating a stochastic process that we
study in detail. We first propose a model for ensembles of realities that do
not change over time. The proposed model is simple in that it enables us to
derive precise coding bounds in the information-theoretic sense that are sharp
in a number of cases of practical interest. For this simple case of static
realities and camera motion, our results indicate that coding practice is in
accordance with optimal coding from an information-theoretic standpoint. The
model is further extended to account for visual realities that change over
time. We derive bounds on the lossless and lossy information rates for this
dynamic reality model, stating conditions under which the bounds are tight.
Examples with synthetic sources suggest that in the presence of scene dynamics,
simple hybrid coding using motion/displacement estimation with DPCM performs
considerably suboptimally relative to the true rate-distortion bound.Comment: submitted to IEEE Transactions in Information Theor
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