595 research outputs found
High-resolution distributed sampling of bandlimited fields with low-precision sensors
The problem of sampling a discrete-time sequence of spatially bandlimited
fields with a bounded dynamic range, in a distributed,
communication-constrained, processing environment is addressed. A central unit,
having access to the data gathered by a dense network of fixed-precision
sensors, operating under stringent inter-node communication constraints, is
required to reconstruct the field snapshots to maximum accuracy. Both
deterministic and stochastic field models are considered. For stochastic
fields, results are established in the almost-sure sense. The feasibility of
having a flexible tradeoff between the oversampling rate (sensor density) and
the analog-to-digital converter (ADC) precision, while achieving an exponential
accuracy in the number of bits per Nyquist-interval per snapshot is
demonstrated. This exposes an underlying ``conservation of bits'' principle:
the bit-budget per Nyquist-interval per snapshot (the rate) can be distributed
along the amplitude axis (sensor-precision) and space (sensor density) in an
almost arbitrary discrete-valued manner, while retaining the same (exponential)
distortion-rate characteristics. Achievable information scaling laws for field
reconstruction over a bounded region are also derived: With N one-bit sensors
per Nyquist-interval, Nyquist-intervals, and total network
bitrate (per-sensor bitrate ), the maximum pointwise distortion goes to zero as
or . This is shown to be possible
with only nearest-neighbor communication, distributed coding, and appropriate
interpolation algorithms. For a fixed, nonzero target distortion, the number of
fixed-precision sensors and the network rate needed is always finite.Comment: 17 pages, 6 figures; paper withdrawn from IEEE Transactions on Signal
Processing and re-submitted to the IEEE Transactions on Information Theor
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
Geometric approach to sampling and communication
Relationships that exist between the classical, Shannon-type, and
geometric-based approaches to sampling are investigated. Some aspects of coding
and communication through a Gaussian channel are considered. In particular, a
constructive method to determine the quantizing dimension in Zador's theorem is
provided. A geometric version of Shannon's Second Theorem is introduced.
Applications to Pulse Code Modulation and Vector Quantization of Images are
addressed.Comment: 19 pages, submitted for publicatio
Quantization and Compressive Sensing
Quantization is an essential step in digitizing signals, and, therefore, an
indispensable component of any modern acquisition system. This book chapter
explores the interaction of quantization and compressive sensing and examines
practical quantization strategies for compressive acquisition systems.
Specifically, we first provide a brief overview of quantization and examine
fundamental performance bounds applicable to any quantization approach. Next,
we consider several forms of scalar quantizers, namely uniform, non-uniform,
and 1-bit. We provide performance bounds and fundamental analysis, as well as
practical quantizer designs and reconstruction algorithms that account for
quantization. Furthermore, we provide an overview of Sigma-Delta
() quantization in the compressed sensing context, and also
discuss implementation issues, recovery algorithms and performance bounds. As
we demonstrate, proper accounting for quantization and careful quantizer design
has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing
and Its Applications", 201
Sub-Nyquist Sampling: Bridging Theory and Practice
Sampling theory encompasses all aspects related to the conversion of
continuous-time signals to discrete streams of numbers. The famous
Shannon-Nyquist theorem has become a landmark in the development of digital
signal processing. In modern applications, an increasingly number of functions
is being pushed forward to sophisticated software algorithms, leaving only
those delicate finely-tuned tasks for the circuit level.
In this paper, we review sampling strategies which target reduction of the
ADC rate below Nyquist. Our survey covers classic works from the early 50's of
the previous century through recent publications from the past several years.
The prime focus is bridging theory and practice, that is to pinpoint the
potential of sub-Nyquist strategies to emerge from the math to the hardware. In
that spirit, we integrate contemporary theoretical viewpoints, which study
signal modeling in a union of subspaces, together with a taste of practical
aspects, namely how the avant-garde modalities boil down to concrete signal
processing systems. Our hope is that this presentation style will attract the
interest of both researchers and engineers in the hope of promoting the
sub-Nyquist premise into practical applications, and encouraging further
research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin
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