3 research outputs found
Distributed Greedy Pursuit Algorithms
For compressed sensing over arbitrarily connected networks, we consider the
problem of estimating underlying sparse signals in a distributed manner. We
introduce a new signal model that helps to describe inter-signal correlation
among connected nodes. Based on this signal model along with a brief survey of
existing greedy algorithms, we develop distributed greedy algorithms with low
communication overhead. Incorporating appropriate modifications, we design two
new distributed algorithms where the local algorithms are based on
appropriately modified existing orthogonal matching pursuit and subspace
pursuit. Further, by combining advantages of these two local algorithms, we
design a new greedy algorithm that is well suited for a distributed scenario.
By extensive simulations we demonstrate that the new algorithms in a sparsely
connected network provide good performance, close to the performance of a
centralized greedy solution.Comment: Submitted to EURASIP Signal Processing Dec. 201
Analysis of Democratic Voting Principles used in Distributed Greedy Algorithms
A key aspect for any greedy pursuit algorithm used in compressed sensing is a
good support-set detection method. For distributed compressed sensing, we
consider a setup where many sensors measure sparse signals that are correlated
via the existence of a signals' intersection support-set. This intersection
support-set is called the joint support-set. Estimation of the joint
support-set has a high impact on the performance of a distributed greedy
pursuit algorithm. This estimation can be achieved by exchanging local
support-set estimates followed by a (consensus) voting method. In this paper we
endeavor for a probabilistic analysis of two democratic voting principle that
we call majority and consensus voting. In our analysis, we first model the
input/output relation of a greedy algorithm (executed locally in a sensor) by a
single parameter known as probability of miss. Based on this model, we analyze
the voting principles and prove that the democratic voting principle has a
merit to detect the joint support-set.Comment: Submitted to Transactions on Signal Processin
Design and Analysis of a Greedy Pursuit for Distributed Compressed Sensing
We consider a distributed compressed sensing scenario where many sensors
measure correlated sparse signals and the sensors are connected through a
network. Correlation between sparse signals is modeled by a partial common
support-set. For such a scenario, the main objective of this paper is to
develop a greedy pursuit algorithm. We develop a distributed parallel pursuit
(DIPP) algorithm based on exchange of information about estimated support-sets
at sensors. The exchange of information helps to improve estimation of the
partial common support-set, that in turn helps to gradually improve estimation
of support-sets in all sensors, leading to a better quality reconstruction
performance. We provide restricted isometry property (RIP) based theoretical
analysis on the algorithm's convergence and reconstruction performance. Under
certain theoretical requirements on the quality of information exchange over
network and RIP parameters of sensor nodes, we show that the DIPP algorithm
converges to a performance level that depends on a scaled additive measurement
noise power (convergence in theory) where the scaling coefficient is a function
of RIP parameters and information processing quality parameters. Using
simulations, we show practical reconstruction performance of DIPP vis-a-vis
amount of undersampling, signal-to-measurement-noise ratios and
network-connectivity conditions.Comment: Sent to IEEE Transaction on Signal Processin