50,468 research outputs found
One-Bit ExpanderSketch for One-Bit Compressed Sensing
Is it possible to obliviously construct a set of hyperplanes H such that you
can approximate a unit vector x when you are given the side on which the vector
lies with respect to every h in H? In the sparse recovery literature, where x
is approximately k-sparse, this problem is called one-bit compressed sensing
and has received a fair amount of attention the last decade. In this paper we
obtain the first scheme that achieves almost optimal measurements and sublinear
decoding time for one-bit compressed sensing in the non-uniform case. For a
large range of parameters, we improve the state of the art in both the number
of measurements and the decoding time
Mean Estimation from One-Bit Measurements
We consider the problem of estimating the mean of a symmetric log-concave
distribution under the constraint that only a single bit per sample from this
distribution is available to the estimator. We study the mean squared error as
a function of the sample size (and hence the number of bits). We consider three
settings: first, a centralized setting, where an encoder may release bits
given a sample of size , and for which there is no asymptotic penalty for
quantization; second, an adaptive setting in which each bit is a function of
the current observation and previously recorded bits, where we show that the
optimal relative efficiency compared to the sample mean is precisely the
efficiency of the median; lastly, we show that in a distributed setting where
each bit is only a function of a local sample, no estimator can achieve optimal
efficiency uniformly over the parameter space. We additionally complement our
results in the adaptive setting by showing that \emph{one} round of adaptivity
is sufficient to achieve optimal mean-square error
Energy Beamforming with One-Bit Feedback
Wireless energy transfer (WET) has attracted significant attention recently
for providing energy supplies wirelessly to electrical devices without the need
of wires or cables. Among different types of WET techniques, the radio
frequency (RF) signal enabled far-field WET is most practically appealing to
power energy constrained wireless networks in a broadcast manner. To overcome
the significant path loss over wireless channels, multi-antenna or
multiple-input multiple-output (MIMO) techniques have been proposed to enhance
the transmission efficiency and distance for RF-based WET. However, in order to
reap the large energy beamforming gain in MIMO WET, acquiring the channel state
information (CSI) at the energy transmitter (ET) is an essential task. This
task is particularly challenging for WET systems, since existing channel
training and feedback methods used for communication receivers may not be
implementable at the energy receiver (ER) due to its hardware limitation. To
tackle this problem, in this paper we consider a multiuser MIMO system for WET,
where a multiple-antenna ET broadcasts wireless energy to a group of
multiple-antenna ERs concurrently via transmit energy beamforming. By taking
into account the practical energy harvesting circuits at the ER, we propose a
new channel learning method that requires only one feedback bit from each ER to
the ET per feedback interval. The feedback bit indicates the increase or
decrease of the harvested energy by each ER between the present and previous
intervals, which can be measured without changing the existing hardware at the
ER. Based on such feedback information, the ET adjusts transmit beamforming in
different training intervals and at the same time obtains improved estimates of
the MIMO channels to ERs by applying a new approach termed analytic center
cutting plane method (ACCPM).Comment: This is the longer version of a paper to appear in IEEE Transactions
on Signal Processin
One-Bit Compressed Sensing by Greedy Algorithms
Sign truncated matching pursuit (STrMP) algorithm is presented in this paper.
STrMP is a new greedy algorithm for the recovery of sparse signals from the
sign measurement, which combines the principle of consistent reconstruction
with orthogonal matching pursuit (OMP). The main part of STrMP is as concise as
OMP and hence STrMP is simple to implement. In contrast to previous greedy
algorithms for one-bit compressed sensing, STrMP only need to solve a convex
and unconstraint subproblem at each iteration. Numerical experiments show that
STrMP is fast and accurate for one-bit compressed sensing compared with other
algorithms.Comment: 16 pages, 7 figure
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