CN112579687B - Marine environment monitoring data compressed sensing online reconstruction method - Google Patents

Marine environment monitoring data compressed sensing online reconstruction method Download PDF

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CN112579687B
CN112579687B CN202011409107.3A CN202011409107A CN112579687B CN 112579687 B CN112579687 B CN 112579687B CN 202011409107 A CN202011409107 A CN 202011409107A CN 112579687 B CN112579687 B CN 112579687B
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芮国胜
刘歌
田文飚
崔田田
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Naval Aeronautical University
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Abstract

The invention discloses an online compressed sensing reconstruction method for marine environment monitoring data. Aiming at the problem that the reconstruction performance of time-varying ocean monitoring data is not high in the traditional compressed sensing method, the ocean measurement data online reconstruction method based on the low-rank regularized sequential compressed sensing is provided. The method includes the steps of firstly adding low-rank performance of data on a spatial structure into an optimization algorithm, constructing a low-rank regular term by combining existing historical data through a sliding window mechanism, establishing a data fidelity term according to the condition that data in overlapping regions of previous and next moments are equal, and finally solving the reconstruction optimization algorithm based on an alternating direction multiplier method. The method can improve the compressed sensing reconstruction performance of the time-varying ocean monitoring data.

Description

Marine environment monitoring data compressed sensing online reconstruction method
Technical Field
The invention relates to a compressed sensing technology, in particular to an online compressed sensing reconstruction method for marine environment monitoring data, and belongs to the technical field of compressed sensing reconstruction.
Background
The ocean is the foundation on which the human beings rely for survival and development, along with the development of productivity and the progress of social civilization, the world economy, science and technology and military strength are improved, the resource demand of the human society is increased day by day, and because 71 percent of the surface of the ocean floor ball is rich in resources and is not fully developed, the vision of various countries is changed from land to ocean, the enthusiasm of developing and utilizing the ocean is high and the conflict of the ocean rights of the ocean is increased. In this context, the problem of monitoring marine environments is beginning to be of widespread concern. Because the scale range of data acquired by means such as satellite remote sensing and radar is too large and the resolution is too low, the sensor network is called as a main means for acquiring marine environment monitoring data.
In a real scene, a sensor network is formed by deploying a plurality of sensors in a certain ocean monitoring area, the same object is continuously sensed, various environment monitoring data are acquired and transmitted to a monitoring center through a certain communication means, and different types of sensing applications are supported. Compared with the land environment, the marine environment has advantages in depth and breadth, but the advantages place higher demands on the deployment of the marine sensor network: on one hand, the ocean range is too large, so that the number of deployed nodes is too large, and the construction cost is too high; on the other hand, how to transmit the collected mass information timely and effectively is also limited by node energy consumption and communication cost. And the sensor network has the characteristics of more sensors, dynamic change of a topological structure, easiness in damage of sensor nodes, limited storage capacity and the like. This determines that a reasonable solution must be found to solve the contradiction between limited energy and data transmission during the operation of the sensor network.
In recent years, Compressed Sensing (CS) provides a new idea for solving the above problems. According to the CS theory, if a signal is sparse in a certain domain, it can be reconstructed from linear measurements of very few raw data as long as certain conditions are met. Bajwa et al first proposed the introduction of the CS theory into the efficient data collection problem of sensor networks, after which, researchers began conducting a great deal of research into the use of CS theory in sensor networks. The existing algorithm can greatly reduce the communication energy consumption overhead and realize the acquisition, transmission and application of data. None of these algorithms take into account correlations created by dynamic changes in the sensor network data collection process. The sequential compression acquisition and progressive reconstruction of the sensor data stream, however, in the process of collecting the sensor time series data, only the dynamic evolution relation of the time domain stream signal before and after is considered, the spatial structure correlation among multiple sensors is not considered, and the reconstruction performance needs to be improved.
Disclosure of Invention
The invention aims to design a compressed sensing-based marine environment monitoring data online reconstruction method, and aims to solve the problem that the reconstruction performance of the traditional compressed sensing method for processing time-varying marine monitoring data is not high. Firstly, designing a sliding window mechanism, combining the existing historical data, and fully utilizing the low-rank property of a matrix to construct a low-rank matrix; then, according to the rule that the data of the overlapping area are equal, an error correction term of the overlapping area is added; and finally, designing a solving method based on an alternating direction multiplier (ADMM) in the process of solving the reconstruction optimization algorithm.
In order to achieve the purpose, the technical scheme adopted by the invention is a compressed sensing online reconstruction method of marine environment monitoring data, which comprises the following steps:
step 1, inputting observation data y at time tt(t-w): (t-1) original data X(t-w):(t-1)And its observed data Y(t-w):(t-1)Constructing an observation data matrix Y (W-1), wherein W represents the size of a sliding window;
step 2, establishing a compressed sensing online reconstruction model as follows:
Figure BDA0002817888770000021
s.t.S(t)＝Ψ(t)-1vec(X(t)),Z(t)＝X(t)
wherein Y (t) ═ Y(t-W):(t-1),yt]，
Figure BDA0002817888770000022
Representing an observation matrix, m representing the number of observations, N representing the length of the signal, and m < N,
Figure BDA0002817888770000023
representing all sensor node data at time t, λ1And λ2Representing regularization parameters, | Z (t) | non-woven calculation*Represents the nuclear norm of the matrix z (t),
Figure BDA0002817888770000024
new matrix of first (W-1) rows representing the spatio-temporal basis Ψ (t), ΨT(W-1) is the time domain basis ΨTOf the first (W-1) row ofSA spatial basis is represented by a number of spatial groups,
Figure BDA0002817888770000025
showing the estimated values of the overlapping areas of the two moments before and after the moment (t-1), Z (t) showing an intermediate variable, S (t) being a sparse representation matrix of X (t),
Figure BDA0002817888770000026
estimates of X (t), S (t), and Z (t), respectively, vec (-) indicating vectorization of the matrix; step 3, utilizing the input ytRapid reconstruction of data x at time ttAnd with input X(t-w):(t-1)Build the data matrix X in the window1(t) initializing parameters as initial data;
step 3, utilizing the input ytRapid reconstruction of data x at time ttAnd with input X(t-w):(t-1)Build the data matrix X in the window1(t) initializing parameters as initial data;
step 4, solving the reconstruction model by adopting an alternating direction multiplier method, rewriting the reconstruction model into an augmented Lagrange form,
Figure BDA0002817888770000027
a and B represent Lagrange multipliers, alpha and beta are penalty parameters, the problem is decomposed into a plurality of subproblems, and iterative solution is respectively carried out on the subproblems to obtain an original data estimation value at the time t
Figure BDA0002817888770000028
And 5, when t is t +1, the sliding window moves forward, data at the time t moves in, data at the time t-w moves out, and an observation data matrix Y (t +1) at the time t +1 is constructed. If T is equal to T, outputting, otherwise, returning to the step 2;
compared with the prior art, the invention has the following advantages:
1. the low-rank constraint is added into an optimization algorithm, a low-rank regular term is constructed by combining the existing historical data, and the data reconstruction can be optimally constrained by fully utilizing the internal structural features of the data;
2. the condition that data in the overlapped area of a matrix formed by the time-varying data in the sliding window are equal is fully utilized, a data fidelity item is established, the characteristics of the time-varying data are added into an optimization constraint, and the reconstruction precision is further improved.
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FIG. 1 is a schematic flow chart of an online compressed sensing reconstruction method for marine environmental data according to the present invention;
FIG. 2 is a schematic view of a sliding window data acquisition;
fig. 3 is a schematic diagram of an observation process of sequential compressed sensing.
Detailed Description
The present invention will be described in more detail with reference to the following examples and the accompanying drawings.
As shown in fig. 1, an embodiment of the invention discloses a method for compressed sensing online reconstruction of marine environmental monitoring data, which comprises the following specific steps:
step 1, inputting observation data y at t momentt(t-w): (t-1) original data X(t-w):(t-1)And its observation data Y(t-w):(t-1)Constructing an observation data matrix Y (w-1);
step 2, establishing a compressed sensing online reconstruction model as follows:
Figure BDA0002817888770000031
s.t.S(t)＝Ψ-1vec(X(t)),Z(t)＝X(t)
wherein, yN(t)∈Rm×1，Φ(t)∈Rm×NM represents the number of observations, N represents the magnitude of the signal, and m < N, xN(t)∈RN×1Represents all sensor node data at time t, λ1And λ2Representing regularization parameters, | X | | non-woven phosphor*Representing the kernel norm of matrix X, w represents the window size,
Figure BDA0002817888770000032
ΨT(w-1) represents taking the time domain base psiTOf the first (w-1) row ofSA spatial basis is represented by a number of spatial groups,
Figure BDA0002817888770000033
an estimated value representing the overlapping area calculated at time (t-1);
step 3, utilizing the transfusionIn ytRapid reconstruction of data x at time ttAnd with input X(t-w):(t-1)Build data matrix X in window1(t) initializing parameters as initial data;
step 4, solving the reconstruction model by adopting an alternating direction multiplier method, rewriting the reconstruction model into an augmented Lagrange form,
Figure BDA0002817888770000041
a and B represent Lagrange multipliers, alpha and beta are penalty parameters, the problem is decomposed into a plurality of subproblems, and iterative solution is respectively carried out on the subproblems to obtain an original data estimated value at the time t
Figure BDA0002817888770000042
The optimization problem is solved by using an alternating direction multiplier method, and an original reconstruction model is divided into a plurality of subproblems to carry out iterative solution. Knowing the data for the kth iteration, the kth (k +1) iteration is updated
Figure BDA0002817888770000043
Figure BDA0002817888770000044
Figure BDA0002817888770000045
Wherein the iteration parameter is Ak+1＝Ak+α(Sk+1(t)-Ψvec(Xk+1(t)))，Bk+1＝Bk+β(Zk+1(t)-Xk+1(t)); all matrices with subscript k (or k +1) represent the values of the original matrix without subscript at the kth (or k +1) iteration. If K > K (K represents the preset maximum iteration number), stopping iteration, and stopping iteration at the moment
Figure BDA0002817888770000046
Is equal to matrix XkThe last column of (t);
the solving method of the neutron problem X (t) in the iterative process comprises the following specific steps:
(1) first, the gradient of the first sub-problem is calculated
Figure BDA0002817888770000047
Derivative and let the derivative equal zero to obtain
Figure BDA0002817888770000048
Wherein
Figure BDA0002817888770000049
In order to further reduce the calculated amount of matrix inverse operation, a conjugate gradient algorithm is adopted to solve an optimal solution;
(2) the solving method of the sub-problem S (t) in the iteration process comprises the following specific steps:
Figure BDA00028178887700000410
this equation is a standard linear least squares problem, the optimal solution being
Figure BDA00028178887700000411
Wherein G ═ 2 λ1Ψ(w-1)TΨ(w-1)+αI)；
(3) The solving method of the neutron problem Z (t) in the iterative process comprises the following specific steps:
solving Z by singular value shrinkage operator methodk+1(t)
Zk+1(t)＝shrink(Xk+1(t)-Bk/β,λ2/β)
Where shrink (H, τ) refers to a function that soft-thresholds the singular values of matrix H at threshold τ.
And step 5, when t is t +1, the sliding window moves forward, the data at the time t moves in, and the data at the time t-w moves out, so as to construct an observation data matrix Y (t +1) at the time t +1, as shown in fig. 2 and fig. 3. If T is equal to T, outputting, otherwise, returning to the step 2;
the above is a detailed description of the present invention in the following detailed description, which is not intended to limit the present invention in form, so that any person skilled in the art can make changes, modifications and substitutions based on the principle and spirit of the present invention after reading the present invention, and the present invention shall fall into the protection scope of the present invention.

Claims (5)

1. A marine environment monitoring data online reconstruction method based on sequential compressed sensing is characterized by comprising the following steps:
step 1, inputting observation data y at t momentt(t-W) raw data X in time period (t-1)(t-W):(t-1)And its observation data Y(t-W):(t-1)Constructing an observation data matrix Y (t), wherein W represents the size of a sliding window;
step 2, establishing a compressed sensing online reconstruction model as follows:
Figure FDA0002817888760000011
s.t.S(t)＝Ψ(t)-1vec(X(t)),Z(t)＝X(t)
wherein Y (t) ═ Y(t-W):(t-1),yt]，
Figure FDA0002817888760000012
Representing an observation matrix, m representing the number of observations, N representing the length of the signal, and m < N,
Figure FDA0002817888760000013
represents all sensor node data at time t, λ1And λ2Representing a regularization parameter, | Z (t) | ventilated computing*Represents the kernel norm of the matrix z (t),
Figure FDA0002817888760000014
new matrix of first (W-1) rows representing the space-time basis Ψ (t), ΨT(W-1) is the time domain basis ΨTOf the first (W-1) row ofSA spatial basis is represented by a number of spatial groups,
Figure FDA0002817888760000015
showing the estimated values of the overlapping areas of the two moments before and after the moment (t-1), Z (t) showing an intermediate variable, S (t) being a sparse representation matrix of X (t),
Figure FDA0002817888760000016
estimated values of x (t), s (t) and z (t), respectively, vec (-) indicating vectorization of the matrix;
step 3, utilizing the input ytRapid reconstruction of data x at time ttAnd with input X(t-w):(t-1)Build the data matrix X in the window1(t) initializing parameters as initial data;
step 4, solving the reconstruction model by adopting an alternating direction multiplier method, rewriting the reconstruction model into an augmented Lagrange form,
Figure FDA0002817888760000017
a and B represent Lagrange multipliers, alpha and beta are penalty parameters, the problem is decomposed into a plurality of subproblems, and iteration solving is carried out respectively to obtain x at t momenttEstimated value
Figure FDA0002817888760000018
And 5, if T is equal to T, outputting, otherwise, returning to the step 2.
2. The method according to claim 1, wherein the method for solving the reconstructed model in step 4 is specifically: dividing the original reconstruction model into a plurality of subproblems to carry out iterative solution, knowing the data of the kth iteration, updating the kth (k +1) iteration process
Figure FDA0002817888760000019
Figure FDA0002817888760000021
Figure FDA0002817888760000022
Wherein the iteration parameter is Ak+1＝Ak+α(Sk+1(t)-Ψ(t)vec(Xk+1(t)))，Bk+1＝Bk+β(Zk+1(t)-Xk+1(t)), if K > K (K represents a predetermined maximum number of iterations), stopping the iteration, at which point
Figure FDA0002817888760000023
Is equal to matrix XkThe last column of (t).
3. The method according to claim 2, wherein the solving method of the neutron problem x (t) in the iterative process is specifically:
first, the gradient of the first sub-problem is calculated
Figure FDA0002817888760000024
Derivative and make the derivative equal to zero to obtain
Figure FDA0002817888760000025
Wherein
Figure FDA0002817888760000026
Figure FDA0002817888760000027
And expressing a unit matrix, and solving an optimal solution by adopting a conjugate gradient algorithm in order to further reduce the calculated amount of matrix inverse operation.
4. The method of claim 2, wherein the solving method of the sub-problem s (t) in the iterative process is specifically:
Figure FDA0002817888760000028
this equation is a standard linear least squares problem, the optimal solution being
Figure FDA0002817888760000029
Wherein G ═ 2 λ1Ψ(w-1)TΨ(w-1)+αI)。
5. The method according to claim 2, wherein the solving method of the neutron problem z (t) in the iterative process is specifically:
solving Z by singular value shrinkage operator methodk+1(t)
Zk+1(t)＝shrink(Xk+1(t)-Bk/β,λ2/β)
Where shrnk (H, τ) refers to a function that soft-thresholds singular values of matrix H at threshold τ.
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