335 research outputs found
Power-Constrained Sparse Gaussian Linear Dimensionality Reduction over Noisy Channels
In this paper, we investigate power-constrained sensing matrix design in a
sparse Gaussian linear dimensionality reduction framework. Our study is carried
out in a single--terminal setup as well as in a multi--terminal setup
consisting of orthogonal or coherent multiple access channels (MAC). We adopt
the mean square error (MSE) performance criterion for sparse source
reconstruction in a system where source-to-sensor channel(s) and
sensor-to-decoder communication channel(s) are noisy. Our proposed sensing
matrix design procedure relies upon minimizing a lower-bound on the MSE in
single-- and multiple--terminal setups. We propose a three-stage sensing matrix
optimization scheme that combines semi-definite relaxation (SDR) programming, a
low-rank approximation problem and power-rescaling. Under certain conditions,
we derive closed-form solutions to the proposed optimization procedure. Through
numerical experiments, by applying practical sparse reconstruction algorithms,
we show the superiority of the proposed scheme by comparing it with other
relevant methods. This performance improvement is achieved at the price of
higher computational complexity. Hence, in order to address the complexity
burden, we present an equivalent stochastic optimization method to the problem
of interest that can be solved approximately, while still providing a superior
performance over the popular methods.Comment: Accepted for publication in IEEE Transactions on Signal Processing
(16 pages
Optimized Compressed Sensing Matrix Design for Noisy Communication Channels
We investigate a power-constrained sensing matrix design problem for a
compressed sensing framework. We adopt a mean square error (MSE) performance
criterion for sparse source reconstruction in a system where the
source-to-sensor channel and the sensor-to-decoder communication channel are
noisy. Our proposed sensing matrix design procedure relies upon minimizing a
lower-bound on the MSE. Under certain conditions, we derive closed-form
solutions to the optimization problem. Through numerical experiments, by
applying practical sparse reconstruction algorithms, we show the strength of
the proposed scheme by comparing it with other relevant methods. We discuss the
computational complexity of our design method, and develop an equivalent
stochastic optimization method to the problem of interest that can be solved
approximately with a significantly less computational burden. We illustrate
that the low-complexity method still outperforms the popular competing methods.Comment: Submitted to IEEE ICC 2015 (EXTENDED VERSION
Performance Limits of Compressive Sensing Channel Estimation in Dense Cloud RAN
Towards reducing the training signaling overhead in large scale and dense
cloud radio access networks (CRAN), various approaches have been proposed based
on the channel sparsification assumption, namely, only a small subset of the
deployed remote radio heads (RRHs) are of significance to any user in the
system. Motivated by the potential of compressive sensing (CS) techniques in
this setting, this paper provides a rigorous description of the performance
limits of many practical CS algorithms by considering the performance of the,
so called, oracle estimator, which knows a priori which RRHs are of
significance but not their corresponding channel values. By using tools from
stochastic geometry, a closed form analytical expression of the oracle
estimator performance is obtained, averaged over distribution of RRH positions
and channel statistics. Apart from a bound on practical CS algorithms, the
analysis provides important design insights, e.g., on how the training sequence
length affects performance, and identifies the operational conditions where the
channel sparsification assumption is valid. It is shown that the latter is true
only in operational conditions with sufficiently large path loss exponents.Comment: 6 pages, two-column format; ICC 201
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
Joint Sensing Matrix and Sparsifying Dictionary Optimization for Tensor Compressive Sensing.
Tensor compressive sensing (TCS) is a multidimensional framework of compressive sensing (CS), and it is
advantageous in terms of reducing the amount of storage, easing
hardware implementations, and preserving multidimensional
structures of signals in comparison to a conventional CS system.
In a TCS system, instead of using a random sensing matrix and
a predefined dictionary, the average-case performance can be
further improved by employing an optimized multidimensional
sensing matrix and a learned multilinear sparsifying dictionary.
In this paper, we propose an approach that jointly optimizes
the sensing matrix and dictionary for a TCS system. For the
sensing matrix design in TCS, an extended separable approach
with a closed form solution and a novel iterative nonseparable
method are proposed when the multilinear dictionary is fixed.
In addition, a multidimensional dictionary learning method that
takes advantages of the multidimensional structure is derived,
and the influence of sensing matrices is taken into account in the
learning process. A joint optimization is achieved via alternately
iterating the optimization of the sensing matrix and dictionary.
Numerical experiments using both synthetic data and real images
demonstrate the superiority of the proposed approache
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