402 research outputs found
Bandlimited Spatial Field Sampling with Mobile Sensors in the Absence of Location Information
Sampling of physical fields with mobile sensor is an emerging area. In this
context, this work introduces and proposes solutions to a fundamental question:
can a spatial field be estimated from samples taken at unknown sampling
locations?
Unknown sampling location, sample quantization, unknown bandwidth of the
field, and presence of measurement-noise present difficulties in the process of
field estimation. In this work, except for quantization, the other three issues
will be tackled together in a mobile-sampling framework. Spatially bandlimited
fields are considered. It is assumed that measurement-noise affected field
samples are collected on spatial locations obtained from an unknown renewal
process. That is, the samples are obtained on locations obtained from a renewal
process, but the sampling locations and the renewal process distribution are
unknown. In this unknown sampling location setup, it is shown that the
mean-squared error in field estimation decreases as where is the
average number of samples collected by the mobile sensor. The average number of
samples collected is determined by the inter-sample spacing distribution in the
renewal process. An algorithm to ascertain spatial field's bandwidth is
detailed, which works with high probability as the average number of samples
increases. This algorithm works in the same setup, i.e., in the presence of
measurement-noise and unknown sampling locations.Comment: Submitted to IEEE Trans on Signal Processin
Transmission of a continuous signal via one-bit capacity channel
We study the problem of the transmission of currently observed time variable
signals via a channel that is capable of sending a single binary signal only
for each measurement of the underlying process. For encoding and decoding, we
suggest a modification othe adaptive delta modulation algorithm. This
modification ensures tracking of time variable signals. We obtained upper
estimates for the error for the case of noiseless transmission
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
Recursive Compressed Sensing
We introduce a recursive algorithm for performing compressed sensing on
streaming data. The approach consists of a) recursive encoding, where we sample
the input stream via overlapping windowing and make use of the previous
measurement in obtaining the next one, and b) recursive decoding, where the
signal estimate from the previous window is utilized in order to achieve faster
convergence in an iterative optimization scheme applied to decode the new one.
To remove estimation bias, a two-step estimation procedure is proposed
comprising support set detection and signal amplitude estimation. Estimation
accuracy is enhanced by a non-linear voting method and averaging estimates over
multiple windows. We analyze the computational complexity and estimation error,
and show that the normalized error variance asymptotically goes to zero for
sublinear sparsity. Our simulation results show speed up of an order of
magnitude over traditional CS, while obtaining significantly lower
reconstruction error under mild conditions on the signal magnitudes and the
noise level.Comment: Submitted to IEEE Transactions on Information Theor
- …