CN106658577B - A kind of Sensor Network data reconstruction method of joint space-time sparsity - Google Patents
A kind of Sensor Network data reconstruction method of joint space-time sparsity Download PDFInfo
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Abstract
A kind of Sensor Network data reconstruction method of joint space-time sparsity, is related to Sensor Network data processing.The following steps are included: 1) building spatio-temporal data indicates；2) joint space-time sparsity Sensor Network data reconstruction model is established；3) the Sensor Network data reconstruction model of joint space-time sparsity is solved.Using sensing network data, spatially the sparsity based on figure and the sparsity on the time based on wavelet transformation carry out data recovery to joint.In the acquisition of wireless sensing network data, node or communication failure may cause sensor signal missing, it is therefore desirable to restore to deleted signal.Sensing node is considered to the vertex in graph theory, the sparse signal representation based on wavelet transformation on the spatially sparse signal representation based on figure and time is established by joint, the deleted signal reconstruction model of space-time is established, signal recovery is then carried out by fast iterative algorithm.
Description
Technical field
The present invention relates to Sensor Network data processings, more particularly, to a kind of joint space-time sparsity sensing netting index
According to restoration methods.
Background technique
Sensor network data is to acquire data by sensor node each in sensor network then to pass through sensor
What network transmission obtained after summarizing.It in practice, is on constant duration to each in space for the sampling of wireless sense network
Acquisition node carries out multiple repairing weld, and sensor node failure and sensor network communication obstacle will lead to sensor network data
Active or missing out.Loss of data can be solved by data re-transmission, but data re-transmission can bring financial burden sum number
According to distortion, so needing to restore missing data signal using the data having received by signal processing.In space point
The sensor closed on cloth is easy to measure similar signal, therefore Sensor Network signal may spatially have sparsity
(D.Guo,X.Qu,L.Huang,and Y.Yao."Optimized local superposition in wireless
sensor networks with t-average-mutual-coherence,"Progress in Electromagnetics
Research,122:389-411,2012.)(Di Guo,X.Qu,L.Huang,and Y.Yao."Sparsity-based
spatial interpolation in wireless wensor networks,"Sensors,11(3):2385-2407,
2011.).In addition, sensing network data is generally slowly varying with the time, so may also have sparsity in time
(D.Guo,Z.Liu,X.Qu,L.Huang,Y.Yao,and M.-T.Sun."Sparsity-based online missing
data recovery using overcomplete dictionary,"IEEE Sensors Journal,12(7):2485-
2495,2012.).Therefore, will sense sparsity of the network data on room and time combine be used in data restore on be ten
Divide significant.
Figure is mainly made of the side on vertex and connection vertex, and the size of numerical value represents the signal of signaling point herein on vertex
Value, Bian Ze represent contiguity or similitude between vertex and vertex.Figure is widely used in scientific research field and social life,
It indicates general data and describes the geometry of data, figure signal processing, applied statistics learns problem and engineering and science neck
There is important application in domain.In view of the sparsity of figure, it can solve the problems, such as that sensing network data restores with figure.By each biography
Vertex of the sensor node as figure, collected data are then the signal values on vertex, the relevance between each sensor node
It can be indicated with side.Therefore sensing network data can be indicated with figure, and sensing network data restores problem and is then converted into the extensive of figure
Multiple problem (G.Puy, N.Tremblay, R.Gribonval, and P.Vandergheynst, " Random sampling of
bandlimited signals on graphs,"Applied and Computational Harmonic Analysis,
2016.)。
Summary of the invention
The purpose of the present invention is to provide a kind of joint space-time sparsity Sensor Network data reconstruction methods.
The present invention the following steps are included:
1) building spatio-temporal data indicates that specific method can are as follows:
With Q sensor, the time carries out data acquisition at equal intervals in certain area of space, acquires K frame altogether；Q-th of sensor
The information that node carriesIt is expressed aspqIt is the spatial position of q-th of sensor node, VqIt (k) is the section
Data that point is acquired in kth frame (k=1,2 ..., K)；In the case where no loss of data, the K frame data of Q sensor can
To constitute a data matrix X, matrix size is Q × K；The kth column of data matrix X indicate k-th of moment all the sensors
Data, the q row of data matrix X indicate q-th of sensor node in the data at total K moment；When in data acquisition
I-th of sensor sets 0 when j-th of time data lacks, by j-th of data point of the i-th row in data matrix X, generates new number
According to matrix Y；It can be expressed as Y=AX with data sampling operator A.
2) joint space-time sparsity Sensor Network data reconstruction model is established, specific method can are as follows:
The distribution of sensor node generally in space is heterogeneous；In view of sensing network data is distributed tool in space
There is sparsity, and also there is sparsity in time, establishes the reconstruction model of deleted signal:
Wherein, DGIt is weighted gradient operator matrix spatially, weight between element representation spatial points, value is to pass
The inverse of the space length of sensor node, is defined as:
T is threshold value；
S expression parameter；Space length on i-th of d (i, j) representation space and j-th of node
Matrix, be defined as d (i, j)=| | ri-rj||2, symbol | | | |2It indicates to seek vector 2 norms, r indicates that the position of signaling point is sat
Mark；PkX indicates to take out the kth column of X；HqX is indicated to take out the q row of X and is carried out transposition；Ψ indicates temporal wavelet transformation；|
|·||1The l of vector is sought in expression1Norm；||·||FIt indicates to Matrix Calculating not this black norm of Luo Beini；β is regularization parameter, with
The sparse item of the common trades space of parameter lambdaTime sparse itemWith data check itemThree importance；β and λ value is all larger than 0.
3) the Sensor Network data reconstruction model of joint space-time sparsity is solved, specific method can are as follows:
In order to solve the problems in formula (1), formula (1) is converted into an accepted way of doing sth (2):
Wherein, matrix
To solve the problems in formula (2), a kind of improved iteratively faster soft-threshold algorithm (Beck.A, and are utilized
Teboulle.M,"Fast gradient-based algorithms for constrained total variation
image denoising and deblurring problems,"IEEE Transactions on Image
Processing,2009,18(11):2419-2434.)(I.Loris,and C.Verhoeven,"On a
generalization of the iterative soft thresholding algorithm for the case of
non-separable penalty,"Inverse Problems,2011,27(12):635-656.).Introduce intermediate variable gr
And Ur(UrThere is identical dimensional with X), the r times iteration is indicated with r, according to formula more new variables:
Wherein, A*Indicate the adjoint operator of A；Parameter L indicates step-length；μ is a given parameters, is defined as μ > 0, be for
Guarantee smoothing of functions；Tλμ(a) it is contraction operator, acts on all elements of vector a, is defined as: Tλμ(ai)=(| ai|-λ
μ)+sgn(ai), aiIt takes all over each element in vector a；When reaching iteration stopping criterion, iteration
Stop, when the iterations cease, the Sensor Network space-time signal that can be restored according to formula (3).
In step 3), the criterion of the iteration stopping be set as reaching maximum number of iterations orIt is less than
The threshold value η of setting, threshold value η value are greater than 0.
The invention reside in joint using sensing network data spatially the sparsity based on figure and on the time based on small echo become
The sparsity changed carries out data recovery.In the acquisition of wireless sensing network data, node or communication failure may cause sensor letter
Number missing, it is therefore desirable to deleted signal is restored.Sensing node is considered the vertex in graph theory by the present invention, passes through joint
Establish the sparse signal representation based on wavelet transformation on the spatially sparse signal representation based on figure and time, establish space-when
Between deleted signal reconstruction model, then pass through fast iterative algorithm carry out signal recovery.
Detailed description of the invention
Fig. 1 is the 1st frame signal after restoring.
Fig. 2 is the 11st frame signal after restoring.
Fig. 3 is the 1st frame signal for not losing data, as reference.
Fig. 4 is the 11st frame signal for not losing data, as reference.
Specific embodiment
Below by specific embodiment, the present invention is described in further detail, and provides the result of reconstruction.This implementation
Example is the simulated experiment that a sensor network data is rebuild.
Step 1: determining the loss of data position of a sensor network, building spatio-temporal data is indicated
In the present embodiment, primary every 0.5h sampling with temperature change in 88 sensor measurement regions one day, altogether
48 frames generate temperature signal matrix X.The temperature data (17%) of 15 sensing data nodes of random loss in each frame is surveyed
The signal matrix measured is denoted as Y.
Step 2: establishing joint space-time sparsity sensing network data Restoration model
There is sparsity simultaneously in space and on the time in view of sensor network data, establish the reconstruction mould of deleted signal
Type:
Wherein, DGIt is weighted gradient operator matrix spatially, weight between element representation spatial points, value is to pass
The inverse of the space length of sensor node, is defined as:
T is threshold value.
S expression parameter；Space length on i-th of d (i, j) representation space and j-th of node
Matrix, be defined as d (i, j)=| | ri-rj||2, symbol | | | |2It indicates to seek vector 2 norms, r indicates that the position of signaling point is sat
Mark.PkX indicates to take out the kth column of X；HqX is indicated to take out the q row of X and is carried out transposition；Ψ indicates temporal wavelet transformation；|
|·||1The l of vector is sought in expression1Norm；||·||FIt indicates to Matrix Calculating not this black norm of Luo Beini；β is regularization parameter, with
The sparse item of the common trades space of parameter lambdaTime sparse itemWith data check item
Three importance.β and λ value is all larger than 0.In the present embodiment, parameter s is set as 0.15, and threshold value T is set as 0.1, and parameter lambda is set as
10-3, β is set as 1.
Step 3: being solved to the Sensor Network data reconstruction model of joint space-time sparsity
In order to solve the problems in formula (1), formula (1) is converted into an accepted way of doing sth (2):
Wherein, matrix
To solve the problems in formula (2), a kind of improved iteratively faster soft-threshold algorithm (Beck.A, and are utilized
Teboulle.M,"Fast gradient-based algorithms for constrained total variation
image denoising and deblurring problems,"IEEE Transactions on Image
Processing,2009,18(11):2419-2434.)(I.Loris,and C.Verhoeven,"On a
generalization of the iterative soft thresholding algorithm for the case of
non-separable penalty,"Inverse Problems,2011,27(12):635-656.).Introduce intermediate variable gr
And Ur(UrThere is identical dimensional with X), the r times iteration is indicated with r, according to formula more new variables:
Wherein A*Indicate the adjoint operator of A；Parameter L is set as 7, indicates step-length；μ is a given parameters, is set asGuarantee smoothing of functions；Tλμ(a) it is contraction operator, acts on all elements of vector a, is defined as: Tλμ(ai)=
(|ai|-λμ)+sgn(ai), aiIt takes all over each element in vector a；When reaching iteration stopping criterion
When, iteration stopping.Iteration stopping criterion be set as reaching maximum number of iterations 2000 orLess than the threshold value of setting
η, η are set as 10-5.When the iterations cease, the Sensor Network space-time signal that can be restored according to formula (3).Is listed herein
1 frame (as shown in Figure 1) and the 11st frame signal (as shown in Figure 2).As reference, we draw the 1st frame (such as Fig. 3 of initial intact
It is shown) and the 11st frame signal (as shown in Figure 4).As can be seen that collected partial data and restoration methods of the invention are utilized,
It can restore to obtain the Sensor Network space-time signal of high quality.
Claims (2)
1. a kind of joint space-time sparsity Sensor Network data reconstruction method, it is characterised in that the following steps are included:
1) building spatio-temporal data indicates, method particularly includes:
With Q sensor, the time carries out data acquisition at equal intervals in certain area of space, acquires K frame altogether；Q-th of sensor node
The information of carryingIt is expressed aspqIt is the spatial position of q-th of sensor node, VqIt (k) is that the node exists
The data (k=1,2 ..., K) of kth frame acquisition；In the case where no loss of data, the K frame data of Q sensor constitute one
A data matrix X, matrix size are Q × K；The kth column of data matrix X indicate the data of k-th of moment all the sensors, data
The q row of matrix X indicates q-th of sensor node in the data at total K moment；When i-th of sensing in data acquisition
Device sets 0 when j-th of time data lacks, by j-th of data point of the i-th row in data matrix X, generates new data matrix Y；With
Data sampling operator A is expressed as Y=AX；
2) joint space-time sparsity Sensor Network data reconstruction model is established, method particularly includes:
The distribution of sensor node generally in space is heterogeneous；In view of sensing network data is distributed with dilute in space
Property is dredged, and also there is sparsity in time, establishes the reconstruction model of deleted signal:
Wherein, DGIt is weighted gradient operator matrix spatially, weight between element representation spatial points, value is sensor
The inverse of the space length of node, is defined as:
T is threshold value；
S expression parameter；Space length matrix on i-th of d (i, j) representation space and j-th of node, it is fixed
Justice be d (i, j)=| | ri-rj||2, symbol | | | |2It indicates to seek vector 2 norms, r indicates the position coordinates of signaling point；PkX table
Show the kth column for taking out X；HqX is indicated to take out the q row of X and is carried out transposition；Ψ indicates temporal wavelet transformation；||·||1Table
Show the l for seeking vector1Norm；||·||FIt indicates to Matrix Calculating not this black norm of Luo Beini；β is regularization parameter, common with parameter lambda
The sparse item of trades spaceTime sparse itemWith data check itemThree weights
The property wanted；β and λ value is all larger than 0；
3) the Sensor Network data reconstruction model of joint space-time sparsity is solved, method particularly includes:
In order to solve the problems in formula (1), formula (1) is converted into an accepted way of doing sth (2):
Wherein, matrix
To solve the problems in formula (2), using a kind of improved iteratively faster soft-threshold algorithm, intermediate variable g is introducedrAnd Ur, Ur
There is identical dimensional with X, indicate the r times iteration with r, according to formula more new variables:
Wherein, A*Indicate the adjoint operator of A；Parameter L indicates step-length；μ is a given parameters, is defined as μ > 0, is to guarantee
Smoothing of functions；Tλμ(a) it is contraction operator, acts on all elements of vector a, is defined as: Tλμ(ai)=(| ai|-λμ)+sgn
(ai), aiIt takes all over each element in vector a；When reaching iteration stopping criterion, iteration stopping,
When the iterations cease, the Sensor Network space-time signal being restored according to formula (3).
2. a kind of Sensor Network data reconstruction method of joint space-time sparsity as described in claim 1, it is characterised in that
In step 3), the iteration stopping criterion be set as reaching maximum number of iterations orLess than the threshold value η of setting, threshold
Value η value is greater than 0.
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