33 research outputs found
Cooperative Sparsity Pattern Recovery in Distributed Networks Via Distributed-OMP
In this paper, we consider the problem of collaboratively estimating the
sparsity pattern of a sparse signal with multiple measurement data in
distributed networks. We assume that each node makes Compressive Sensing (CS)
based measurements via random projections regarding the same sparse signal. We
propose a distributed greedy algorithm based on Orthogonal Matching Pursuit
(OMP), in which the sparse support is estimated iteratively while fusing
indices estimated at distributed nodes. In the proposed distributed framework,
each node has to perform less number of iterations of OMP compared to the
sparsity index of the sparse signal. Thus, with each node having a very small
number of compressive measurements, a significant performance gain in support
recovery is achieved via the proposed collaborative scheme compared to the case
where each node estimates the sparsity pattern independently and then fusion is
performed to get a global estimate. We further extend the algorithm to estimate
the sparsity pattern in a binary hypothesis testing framework, where the
algorithm first detects the presence of a sparse signal collaborating among
nodes with a fewer number of iterations of OMP and then increases the number of
iterations to estimate the sparsity pattern only if the signal is detected
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
Sparse Signal Detection with Compressive Measurements via Partial Support Set Estimation
In this paper, we consider the problem of sparse signal detection based on
partial support set estimation with compressive measurements in a distributed
network. Multiple nodes in the network are assumed to observe sparse signals
which share a common but unknown support. While in the traditional compressive
sensing (CS) framework, the goal is to recover the complete sparse signal, in
sparse signal detection, complete signal recovery may not be necessary to make
a reliable detection decision. In particular, detection can be performed based
on partially or inaccurately estimated signals which requires less
computational burden than that is required for complete signal recovery. To
that end, we investigate the problem of sparse signal detection based on
partially estimated support set. First, we discuss how to determine the minimum
fraction of the support set to be known so that a desired detection performance
is achieved in a centralized setting. Second, we develop two distributed
algorithms for sparse signal detection when the raw compressed observations are
not available at the central fusion center. In these algorithms, the final
decision statistic is computed based on locally estimated partial support sets
via orthogonal matching pursuit (OMP) at individual nodes. The proposed
distributed algorithms with less communication overhead are shown to provide
comparable performance (sometimes better) to the centralized approach when the
size of the estimated partial support set is very small
Robust Detection of Random Events with Spatially Correlated Data in Wireless Sensor Networks via Distributed Compressive Sensing
In this paper, we exploit the theory of compressive sensing to perform
detection of a random source in a dense sensor network. When the sensors are
densely deployed, observations at adjacent sensors are highly correlated while
those corresponding to distant sensors are less correlated. Thus, the
covariance matrix of the concatenated observation vector of all the sensors at
any given time can be sparse where the sparse structure depends on the network
topology and the correlation model. Exploiting the sparsity structure of the
covariance matrix, we develop a robust nonparametric detector to detect the
presence of the random event using a compressed version of the data collected
at the distributed nodes. We employ the multiple access channel (MAC) model
with distributed random projections for sensors to transmit observations so
that a compressed version of the observations is available at the fusion
center. Detection is performed by constructing a decision statistic based on
the covariance information of uncompressed data which is estimated using
compressed data. The proposed approach does not require any knowledge of the
noise parameter to set the threshold, and is also robust when the distributed
random projection matrices become sparse
Wireless Compressive Sensing Over Fading Channels with Distributed Sparse Random Projections
We address the problem of recovering a sparse signal observed by a resource
constrained wireless sensor network under channel fading. Sparse random
matrices are exploited to reduce the communication cost in forwarding
information to a fusion center. The presence of channel fading leads to
inhomogeneity and non Gaussian statistics in the effective measurement matrix
that relates the measurements collected at the fusion center and the sparse
signal being observed. We analyze the impact of channel fading on nonuniform
recovery of a given sparse signal by leveraging the properties of heavy-tailed
random matrices. We quantify the additional number of measurements required to
ensure reliable signal recovery in the presence of nonidentical fading channels
compared to that is required with identical Gaussian channels. Our analysis
provides insights into how to control the probability of sensor transmissions
at each node based on the channel fading statistics in order to minimize the
number of measurements collected at the fusion center for reliable sparse
signal recovery. We further discuss recovery guarantees of a given sparse
signal with any random projection matrix where the elements are sub-exponential
with a given sub-exponential norm. Numerical results are provided to
corroborate the theoretical findings
Subspace Recovery from Structured Union of Subspaces
Lower dimensional signal representation schemes frequently assume that the
signal of interest lies in a single vector space. In the context of the
recently developed theory of compressive sensing (CS), it is often assumed that
the signal of interest is sparse in an orthonormal basis. However, in many
practical applications, this requirement may be too restrictive. A
generalization of the standard sparsity assumption is that the signal lies in a
union of subspaces. Recovery of such signals from a small number of samples has
been studied recently in several works. Here, we consider the problem of
subspace recovery in which our goal is to identify the subspace (from the
union) in which the signal lies using a small number of samples, in the
presence of noise. More specifically, we derive performance bounds and
conditions under which reliable subspace recovery is guaranteed using maximum
likelihood (ML) estimation. We begin by treating general unions and then obtain
the results for the special case in which the subspaces have structure leading
to block sparsity. In our analysis, we treat both general sampling operators
and random sampling matrices. With general unions, we show that under certain
conditions, the number of measurements required for reliable subspace recovery
in the presence of noise via ML is less than that implied using the restricted
isometry property which guarantees signal recovery. In the special case of
block sparse signals, we quantify the gain achievable over standard sparsity in
subspace recovery. Our results also strengthen existing results on sparse
support recovery in the presence of noise under the standard sparsity model
Collaborative Compressive Detection with Physical Layer Secrecy Constraints
This paper considers the problem of detecting a high dimensional signal (not
necessarily sparse) based on compressed measurements with physical layer
secrecy guarantees. First, we propose a collaborative compressive detection
(CCD) framework to compensate for the performance loss due to compression with
a single sensor. We characterize the trade-off between dimensionality reduction
achieved by a universal compressive sensing (CS) based measurement scheme and
the achievable performance of CCD analytically. Next, we consider a scenario
where the network operates in the presence of an eavesdropper who wants to
discover the state of the nature being monitored by the system. To keep the
data secret from the eavesdropper, we propose to use cooperating trustworthy
nodes that assist the fusion center (FC) by injecting artificial noise to
deceive the eavesdropper. We seek the answers to the questions: Does CS help
improve the security performance in such a framework? What are the optimal
values of parameters which maximize the CS based collaborative detection
performance at the FC while ensuring perfect secrecy at the eavesdropper
Recovery of Sparse Matrices via Matrix Sketching
In this paper, we consider the problem of recovering an unknown sparse matrix
X from the matrix sketch Y = AX B^T. The dimension of Y is less than that of X,
and A and B are known matrices. This problem can be solved using standard
compressive sensing (CS) theory after converting it to vector form using the
Kronecker operation. In this case, the measurement matrix assumes a Kronecker
product structure. However, as the matrix dimension increases the associated
computational complexity makes its use prohibitive. We extend two algorithms,
fast iterative shrinkage threshold algorithm (FISTA) and orthogonal matching
pursuit (OMP) to solve this problem in matrix form without employing the
Kronecker product. While both FISTA and OMP with matrix inputs are shown to be
equivalent in performance to their vector counterparts with the Kronecker
product, solving them in matrix form is shown to be computationally more
efficient. We show that the computational gain achieved by FISTA with matrix
inputs over its vector form is more significant compared to that achieved by
OMP
Decentralized and Collaborative Subspace Pursuit: A Communication-Efficient Algorithm for Joint Sparsity Pattern Recovery with Sensor Networks
In this paper, we consider the problem of joint sparsity pattern recovery in
a distributed sensor network. The sparse multiple measurement vector signals
(MMVs) observed by all the nodes are assumed to have a common (but unknown)
sparsity pattern. To accurately recover the common sparsity pattern in a
decentralized manner with a low communication overhead of the network, we
develop an algorithm named decentralized and collaborative subspace pursuit
(DCSP). In DCSP, each node is required to perform three kinds of operations per
iteration: 1) estimate the local sparsity pattern by finding the subspace that
its measurement vector most probably lies in; 2) share its local sparsity
pattern estimate with one-hop neighboring nodes; and 3) update the final
sparsity pattern estimate by majority vote based fusion of all the local
sparsity pattern estimates obtained in its neighborhood. The convergence of
DCSP is proved and its communication overhead is quantitatively analyzed. We
also propose another decentralized algorithm named generalized DCSP (GDCSP) by
allowing more information exchange among neighboring nodes to further improve
the accuracy of sparsity pattern recovery at the cost of increased
communication overhead. Experimental results show that, 1) compared with
existing decentralized algorithms, DCSP provides much better accuracy of
sparsity pattern recovery at a comparable communication cost; and 2) the
accuracy of GDCSP is very close to that of centralized processing.Comment: 30 pages, 9 figure
Joint Sparsity Pattern Recovery with 1-bit Compressive Sensing in Sensor Networks
We study the problem of jointly sparse support recovery with 1-bit
compressive measurements in a sensor network. Sensors are assumed to observe
sparse signals having the same but unknown sparse support. Each sensor
quantizes its measurement vector element-wise to 1-bit and transmits the
quantized observations to a fusion center. We develop a computationally
tractable support recovery algorithm which minimizes a cost function defined in
terms of the likelihood function and the norm. We observe that
even with noisy 1-bit measurements, jointly sparse support can be recovered
accurately with multiple sensors each collecting only a small number of
measurements.Comment: 5 pages, 6 figures, submitted in Asilomar Conference 201