Low-redundancy CS Measurement Method And Its Application In Data Gathering Of WSNs

Compressed sensing (CS) theory, proposed by D. Donoho, E. Candes, T. Tao and others in2006, is a new information acquirement theory integrating sampling and compression. Sincethe data processing system under CS can use the essential characteristics of sparse signal,capture the information of high dimensional signal by low dimensional projections, and thenextract high dimensional signal information from those projections, it is widely concerned andstudied by domestic and international scholars in a few years. Despite CS research in fullswing, it is still not clear for some basic problems. For example, how to get reliablereconstruction compressive observations? Compressive observations can be compressed again?How to design the whole scheme including observation, storage and transmission? How toconstruct measurement matrix easy to implement?For the above problems, based on signal acquisition and processing theory and combinedwith set theory, control theory and information theory, this dissertation proposes thelow-redundancy CS measurement methods by two kinds of ways and obtains reliablereconstruction results by adding the judgment processing mechanism with feedback. And thenreliable low-redundancy measurement methods are applied to data gathering of wirelesssensor networks (WSNs) to save the energy consumption of sensor nodes and achieve reliablereconstruction results. The main researching results of this dissertation are listed as follows.1. Proposing a low-redundancy measurement method for excess initial measurements.For the difficult problem that traditional compression methods are difficult to efficientlyreduce compressed sensing measurements, we propose a method to obtain thelow-redundancy compressed sensing measurements based on mutual coherence theory, settheory and sequential compressed sensing. The proposed method can greatly reduce the costsof storing and transmitting the measurements, which laid the theoretical basis on the design ofthe whole scheme involving observation, storage and transmission.2. Proposing a method of acquiring low-redundancy and reliable measurements forarbitrary initial Gaussian measurements.In traditional methods, compressive measurements may be redundant or containnon-enough information to reconstruct the signal. It will lead to two undesired results that theacquired measurements are high-redundancy or cannot be used to perfectly reconstruct thesignal in practical settings. To deal with those two cases, we propose a method to achievelow-redundancy CS measurements with reconstruction probability1for arbitrary initialGaussian measurements based on information theory, set theory, sequential compressed sensing and the feature of Gaussian measurements. The proposed method has threeadvantages: reducing the data of online storage and transmission, achieving the measurementswith reconstruction probability1and avoiding the difficult problem of estimating the signalsparsity at the expense of accept computational costs. This method provides a definite clue todesign the whole scheme involving observation, storage and transmission.3. Proposing a method of acquiring few measurements with the constraint ofreconstruction probability for initial Bernoulli measurements.For the difficult problem that the existing methods cannot obtain the measurements with theconstraint of reconstruction probability, we focus on the Bernoulli measurements, and proposea method to achieve few measurements with the constraint of reconstruction probability byutilizing the reconstruction feature of Bernoulli measurements, sequential CS and the idea ofreducing redundant measurements. Because the proposed method is suitable for the arbitraryinitial Bernoulli measurements, it can achieve fewer measurements satisfying the constraint ofreconstruction probability whether the sparsity of the signal is known or not. It provides a newclue to the difficult problem of acquire the measurements with the constraint of reconstructionprobability.4. Constructing the deterministic sparse sensing matrices satisfying StRIP via RLDPC.For the redundancy of compressive measurements caused by the superposition of toomuch signal components, we design a class of deterministic sparse sensing matrices withstatistical versions of restricted isometry property (StRIP) via regular low density parity check(RLDPC) matrices. Besides StRIP, the constructed sensing matrices have the same scale ofmeasurement numbers as the dense measurement ensembles. So it is possible to achievelow-redundancy measurements. The designed matrices can be applied to the case that thesamplers have to be the deterministic matrices. And it can be used to reduce the computationalcomplexity and the storage space. Based on the constructed sensing matrices, we design ameasure system with low sampling rate by combining with multi-channel sampling scheme. Itprovides a clear scheme to design the deterministic sparse sensing matrices and themeasurement system with low sampling rate.5. Proposing data gathering of WSNs based on sequential CS and sparse sensing.In order to solve the problem of sensor nodes with limited energy supply in WSNs, weproposed an efficient and reliable method to collect the data of sensor nodes based onsequential CS and sparse sensing. In the proposed method, the data of sensor nodes areselectively collected in a sequence way. When the collecting data arrive at a certain amount, the sink node will extract information and make a decision to collect or not until theagreement rule is satisfied. Since the proposed method adds the computations in the sink nodewith strong computation capacity and decreases the collected data to further reduce the energyconsumption of sensor nodes, it is feasible in practical applications. Also since the proposedmethod adds the judgment mechanism in the sink node, it can obtain reliable reconstructionresults. Therefore, this method can not only reduce the energy consumption of sensor nodes,but also obtain more reliable results without lowering the quality of signal reconstruction. Itwill play an important role in data gathering of WSNs.To sum up, this dissertation designs the sensing matrix and sampling system with strongerpracticability, proposes low-redundancy measurement method with reliable reconstruction,points to that the experience measurements still have considerable redundancy and providessome methods to reduce compressive measurements. These will lay the basis on the design ofthe whole scheme involving observation, storage and transmission. Finally, we apply thosereliable and low redundancy measurement methods to data gathering of WSNs to save theenergy consumption of the sensor nodes and furthrt prolong the lifecycle of WSNs.