Research On Sparse Signal Reconstruction In Wireless Sensor Networks

Wireless Sensor Networks(WSNs)is one of the main constitutions of Internet of Things(IoT).WSNs have been widely used in environmental monitoring and protection,medical care,military field,target tracking and other related areas.However,WSNs is a resource-constrained and error-prone distributed system,which composed of large number of nodes with limited energy,bandwidth,storage and processing ability.In recent years,Compressed Sensing(CS)theory has been proposed,which has opened up a new research avenue for the signal sampling and information acquisition.Compared with traditional Nyquist paradigm,CS framework can recover the signals from far fewer measurements than is possible employing Nyquist sampling rate.Unfortunately,CS only considers recovery of single signals.In case of multi-signals,CS only exploits the intra-signal correlations,without taking the correlations of the multi-signals into account.The correlations are helpful to promote the precision and efficiency of recovery.For exploiting the correlations of the multi-signals,the theory of distributed compressed sensing(DCS)arise in recent years.DCS is seen as the combination of distributed source coding(DSC)and CS.DCS compresses multi-signals independently but recoveries them jointly.By taking advantage of the inter-and intra-signal correlations,DCS can decrease a large number of measurements,especially when the common part of the signals dominates.On the other hand,there are two scheme for joint signal reconstruction at decoder.For the centralized approach to joint signal reconstruction in DCS,all the data needs to be communicated to a fusion centre(FC)for processing.However,this scheme has the following drawbacks: i)the pressure on storage and computation load at the FC tends to increase as the number of nodes grows;ii)sensitive or private local data is exposed to the FC;iii)it cannot be applied in a fusion-centre-free scenario.Decentralized processing in networked sensing systems avoids these drawbacks,and thus is attractive for DCS.There are many challenges need to be studied.In this dissertation,we carried out the related researches on CS based compressive data gathering in WSNs.Our main contributions are follows:1.Aiming at common signal model,we propose a distributed variational Bayesian sparse learning algorithm for fusion-centre-free WSNs.In our scheme,we first present a decentralized spatial-temporal data partition Bayesian probabilistic model.Based on the probabilistic model,a full Vraitional Bayesian(VB)inference is derived for centralized solution and then average-consensus algorithm is employed to obtain the equivalent distributed implementation.Specifically,each node only executes one-step average-consensus with its neighbors per VB step and thus reaches a consensus on estimate of sparse signal finally.In order to reduce the communication cost and computational complexity,the idea of FV-SBL is also introduced to improve the efficiency of algorithm.The proposed approach is ease of implementation and scalability to large-scale networks.In addition,due to the observability of nodes can be enhanced by average-consenus,the number of measurements for each node can be further reduced and not necessary to satisfy lower bound required by CS.Simulation results demonstrate that the proposed distributed approach have good recovery performance and converge to their centralized counterpart.2.Due to the limitations of Common Signal Model,we remove to JSM-2 model for distributed scenarios.We also propose a variational Bayesian algorithm and discuss the parallel processing under distributed convex optimization framework.The variational optimization is redefined as a constrained minimization problem.We separately analyze the convergence of the Alternating Directions Method of Multipliers(ADMM)used in our proposed algorith.To reduce the amount of inter-node communication cost,we further develop a fast distributed VB algorithm with once ADMM iteration needed in each VB step.Our proposed approach is well suited for applications where the privacy of the signal coefficients is important,as there is no direct exchange of either measurements or signal coefficients between the nodes.3.Based on more general JSM-1 model,a robust distributed recovery problem is considered.The signal ensembles follow the JSM-1 model,where each sparse signal consists of common component and innovation component.The signals are measured by WSNs with the presence of outliers.The unknown measurement noise is endowed with the Sudent-t distribution,and then a robust Bayesian probabilistic model is presented.In order to solve the problem,we adopt variational optimation and integrated stochastic natural gradient method for distributed inference in natural parameter space.The numerical simulations demonstrate that the proposed algorithm has comparable recovery performance and convergence properties both with and without the presence of outliers.4.Based on common signal model,we take into accounted the recursive distributed reconstruction problem for time sequence of sparse signals from compressive nosiy measurements.This problem can arise in real-time WSNs applications for multi-dimension signal.The signals are assumed to be sparse in some transform domain and their sparity patterns can change with time gradually.The time sequence of sparse signal satisfies some state space model.Thus,this dynamic problem can be treated as state constrained filtering problem.Pseudo-Measurement(PM)technology is adopted to formulate the sparsity constraint as PM equation embedded filtering method.By exploiting PM and consensus filter,we develop a distributed nonlinear filtering for sparse state estimation based on Cubature Kalman Filter(CKF).This reconstruction algorithm can make all the nodes reach consensus estimate on time-varing sparse signal.Moreover,square-root version is further developed to improve the performance and strengthen power saving capability.5.Based on common signal model,we study centralized reconstruction of time sequence of sparse signals from compressive nosiy measurements with severely bandwidth and energy constrints.Each node adopts an adaptive quantization strategy to coarsely quantize its innovations and transmits them to the fusion center.Subsequently,the non-Gaussian problems caused by quantization are solved by using a novel partical filtering to design a recursive reconstruction algorithm with augmented measurements in the centralized fusion framework.To recover the sparse pattern of estimate by particle filter,we impose the sparse constrait on the filter estimate by means of two methods.Numerical simulation demonstrates that the proposed algorithms provide performance which is comparable to that of the full information(i.e.,unquantized)filtering schemes even in the case where only 1-bit is transmitted to the fusion center.