2,507 research outputs found
Application of Compressive Sensing Techniques in Distributed Sensor Networks: A Survey
In this survey paper, our goal is to discuss recent advances of compressive
sensing (CS) based solutions in wireless sensor networks (WSNs) including the
main ongoing/recent research efforts, challenges and research trends in this
area. In WSNs, CS based techniques are well motivated by not only the sparsity
prior observed in different forms but also by the requirement of efficient
in-network processing in terms of transmit power and communication bandwidth
even with nonsparse signals. In order to apply CS in a variety of WSN
applications efficiently, there are several factors to be considered beyond the
standard CS framework. We start the discussion with a brief introduction to the
theory of CS and then describe the motivational factors behind the potential
use of CS in WSN applications. Then, we identify three main areas along which
the standard CS framework is extended so that CS can be efficiently applied to
solve a variety of problems specific to WSNs. In particular, we emphasize on
the significance of extending the CS framework to (i). take communication
constraints into account while designing projection matrices and reconstruction
algorithms for signal reconstruction in centralized as well in decentralized
settings, (ii) solve a variety of inference problems such as detection,
classification and parameter estimation, with compressed data without signal
reconstruction and (iii) take practical communication aspects such as
measurement quantization, physical layer secrecy constraints, and imperfect
channel conditions into account. Finally, open research issues and challenges
are discussed in order to provide perspectives for future research directions
Bernoulli-Gaussian Approximate Message-Passing Algorithm for Compressed Sensing with 1D-Finite-Difference Sparsity
This paper proposes a fast approximate message-passing (AMP) algorithm for
solving compressed sensing (CS) recovery problems with 1D-finite-difference
sparsity in term of MMSE estimation. The proposed algorithm, named ssAMP-BGFD,
is low-computational with its fast convergence and cheap per-iteration cost,
providing phase transition nearly approaching to the state-of-the-art. The
proposed algorithm is originated from a sum-product message-passing rule,
applying a Bernoulli-Gaussian (BG) prior, seeking an MMSE solution. The
algorithm construction includes not only the conventional AMP technique for the
measurement fidelity, but also suggests a simplified message-passing method to
promote the signal sparsity in finite-difference. Furthermore, we provide an
EM-tuning methodology to learn the BG prior parameters, suggesting how to use
some practical measurement matrices satisfying the RIP requirement under the
ssAMP-BGFD recovery. Extensive empirical results confirms performance of the
proposed algorithm, in phase transition, convergence speed, and CPU runtime,
compared to the recent algorithms.Comment: 17 pages, 13 figures, submitted to the IEEE Transactions on Signal
Processin
An Approach to Complex Bayesian-optimal Approximate Message Passing
In this work we aim to solve the compressed sensing problem for the case of a
complex unknown vector by utilizing the Bayesian-optimal structured signal
approximate message passing (BOSSAMP) algorithm on the jointly sparse real and
imaginary parts of the unknown. By introducing a latent activity variable,
BOSSAMP separates the tasks of activity detection and value estimation to
overcome the problem of detecting different supports in the real and imaginary
parts. We complement the recovery algorithm by two novel support detection
schemes that utilize the updated auxiliary variables of BOSSAMP. Simulations
show the superiority of our proposed method against approximate message passing
(AMP) and its Bayesian-optimal sibling (BAMP), both in mean squared error and
support detection performance
An Approximate Message Passing Framework for Side Information
Approximate message passing (AMP) methods have gained recent traction in
sparse signal recovery. Additional information about the signal, or \emph{side
information} (SI), is commonly available and can aid in efficient signal
recovery. This work presents an AMP-based framework that exploits SI and can be
readily implemented in various settings for which the SI results in separable
distributions. To illustrate the simplicity and applicability of our approach,
this framework is applied to a Bernoulli-Gaussian (BG) model and a time-varying
birth-death-drift (BDD) signal model, motivated by applications in channel
estimation. We develop a suite of algorithms, called AMP-SI, and derive
denoisers for the BDD and BG models. Numerical evidence demonstrating the
advantages of our approach are presented alongside empirical evidence of the
accuracy of a proposed state evolution
From Denoising to Compressed Sensing
A denoising algorithm seeks to remove noise, errors, or perturbations from a
signal. Extensive research has been devoted to this arena over the last several
decades, and as a result, today's denoisers can effectively remove large
amounts of additive white Gaussian noise. A compressed sensing (CS)
reconstruction algorithm seeks to recover a structured signal acquired using a
small number of randomized measurements. Typical CS reconstruction algorithms
can be cast as iteratively estimating a signal from a perturbed observation.
This paper answers a natural question: How can one effectively employ a generic
denoiser in a CS reconstruction algorithm? In response, we develop an extension
of the approximate message passing (AMP) framework, called Denoising-based AMP
(D-AMP), that can integrate a wide class of denoisers within its iterations. We
demonstrate that, when used with a high performance denoiser for natural
images, D-AMP offers state-of-the-art CS recovery performance while operating
tens of times faster than competing methods. We explain the exceptional
performance of D-AMP by analyzing some of its theoretical features. A key
element in D-AMP is the use of an appropriate Onsager correction term in its
iterations, which coerces the signal perturbation at each iteration to be very
close to the white Gaussian noise that denoisers are typically designed to
remove
Graphical Models Concepts in Compressed Sensing
This paper surveys recent work in applying ideas from graphical models and
message passing algorithms to solve large scale regularized regression
problems. In particular, the focus is on compressed sensing reconstruction via
ell_1 penalized least-squares (known as LASSO or BPDN). We discuss how to
derive fast approximate message passing algorithms to solve this problem.
Surprisingly, the analysis of such algorithms allows to prove exact
high-dimensional limit results for the LASSO risk.
This paper will appear as a chapter in a book on `Compressed Sensing' edited
by Yonina Eldar and Gitta Kutyniok.Comment: 43 pages, 22 eps figures, typos correcte
Spatio-temporal Spike and Slab Priors for Multiple Measurement Vector Problems
We are interested in solving the multiple measurement vector (MMV) problem
for instances, where the underlying sparsity pattern exhibit spatio-temporal
structure motivated by the electroencephalogram (EEG) source localization
problem. We propose a probabilistic model that takes this structure into
account by generalizing the structured spike and slab prior and the associated
Expectation Propagation inference scheme. Based on numerical experiments, we
demonstrate the viability of the model and the approximate inference scheme.Comment: 6 pages, 6 figures, accepted for presentation at SPARS 201
Hyperspectral Unmixing via Turbo Bilinear Approximate Message Passing
The goal of hyperspectral unmixing is to decompose an electromagnetic
spectral dataset measured over M spectral bands and T pixels into N constituent
material spectra (or "end-members") with corresponding spatial abundances. In
this paper, we propose a novel approach to hyperspectral unmixing based on
loopy belief propagation (BP) that enables the exploitation of spectral
coherence in the endmembers and spatial coherence in the abundances. In
particular, we partition the factor graph into spectral coherence, spatial
coherence, and bilinear subgraphs, and pass messages between them using a
"turbo" approach. To perform message passing within the bilinear subgraph, we
employ the bilinear generalized approximate message passing algorithm
(BiG-AMP), a recently proposed belief-propagation-based approach to matrix
factorization. Furthermore, we propose an expectation-maximization (EM)
strategy to tune the prior parameters and a model-order selection strategy to
select the number of materials N. Numerical experiments conducted with both
synthetic and real-world data show favorable unmixing performance relative to
existing methods
A GAMP Based Low Complexity Sparse Bayesian Learning Algorithm
In this paper, we present an algorithm for the sparse signal recovery problem
that incorporates damped Gaussian generalized approximate message passing
(GGAMP) into Expectation-Maximization (EM)-based sparse Bayesian learning
(SBL). In particular, GGAMP is used to implement the E-step in SBL in place of
matrix inversion, leveraging the fact that GGAMP is guaranteed to converge with
appropriate damping. The resulting GGAMP-SBL algorithm is much more robust to
arbitrary measurement matrix than the standard damped GAMP
algorithm while being much lower complexity than the standard SBL algorithm. We
then extend the approach from the single measurement vector (SMV) case to the
temporally correlated multiple measurement vector (MMV) case, leading to the
GGAMP-TSBL algorithm. We verify the robustness and computational advantages of
the proposed algorithms through numerical experiments
Low-Complexity Message Passing Based Massive MIMO Channel Estimation by Exploiting Unknown Sparse Common Support with Dirichlet Process
This paper investigates the problem of estimating sparse channels in massive
MIMO systems. Most wireless channels are sparse with large delay spread, while
some channels can be observed having sparse common support (SCS) within a
certain area of the antenna array, i.e., the antenna array can be grouped into
several clusters according to the sparse supports of channels. The SCS property
is attractive when it comes to the estimation of large number of channels in
massive MIMO systems. Using the SCS of channels, one expects better
performance, but the number of clusters and the elements for each cluster are
always unknown in the receiver. In this paper, {the Dirichlet process} is
exploited to model such sparse channels where those in each cluster have SCS.
We proposed a low complexity message passing based sparse Bayesian learning to
perform channel estimation in massive MIMO systems by using combined BP with MF
on a factor graph. Simulation results demonstrate that the proposed massive
MIMO sparse channel estimation outperforms the state-of-the-art algorithms.
Especially, it even shows better performance than the variational Bayesian
method applied for massive MIMO channel estimation.Comment: arXiv admin note: text overlap with arXiv:1409.4671 by other author
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