7,616 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
Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences
Compressive sensing (CS) has recently emerged as a framework for efficiently
capturing signals that are sparse or compressible in an appropriate basis.
While often motivated as an alternative to Nyquist-rate sampling, there remains
a gap between the discrete, finite-dimensional CS framework and the problem of
acquiring a continuous-time signal. In this paper, we attempt to bridge this
gap by exploiting the Discrete Prolate Spheroidal Sequences (DPSS's), a
collection of functions that trace back to the seminal work by Slepian, Landau,
and Pollack on the effects of time-limiting and bandlimiting operations. DPSS's
form a highly efficient basis for sampled bandlimited functions; by modulating
and merging DPSS bases, we obtain a dictionary that offers high-quality sparse
approximations for most sampled multiband signals. This multiband modulated
DPSS dictionary can be readily incorporated into the CS framework. We provide
theoretical guarantees and practical insight into the use of this dictionary
for recovery of sampled multiband signals from compressive measurements
Measurement Bounds for Sparse Signal Ensembles via Graphical Models
In compressive sensing, a small collection of linear projections of a sparse
signal contains enough information to permit signal recovery. Distributed
compressive sensing (DCS) extends this framework by defining ensemble sparsity
models, allowing a correlated ensemble of sparse signals to be jointly
recovered from a collection of separately acquired compressive measurements. In
this paper, we introduce a framework for modeling sparse signal ensembles that
quantifies the intra- and inter-signal dependencies within and among the
signals. This framework is based on a novel bipartite graph representation that
links the sparse signal coefficients with the measurements obtained for each
signal. Using our framework, we provide fundamental bounds on the number of
noiseless measurements that each sensor must collect to ensure that the signals
are jointly recoverable.Comment: 11 pages, 2 figure
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