Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 187095, 9 pages

http://dx.doi.org/10.1155/2015/187095

## WSNs Microseismic Signal Subsection Compression Algorithm Based on Compressed Sensing

^{1}School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China^{2}Xi’an Aeronautical University, Xi’an 710077, China

Received 2 March 2015; Revised 30 April 2015; Accepted 3 May 2015

Academic Editor: Ming-Hung Hsu

Copyright © 2015 Zhouzhou Liu and Fubao Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

For wireless network microseismic monitoring and the problems of low compression ratio and high energy consumption of communication, this paper proposes a segmentation compression algorithm according to the characteristics of the microseismic signals and the compression perception theory (CS) used in the transmission process. The algorithm will be collected as a number of nonzero elements of data segmented basis, by reducing the number of combinations of nonzero elements within the segment to improve the accuracy of signal reconstruction, while taking advantage of the characteristics of compressive sensing theory to achieve a high compression ratio of the signal. Experimental results show that, in the quantum chaos immune clone refactoring (Q-CSDR) algorithm for reconstruction algorithm, under the condition of signal sparse degree higher than 40, to be more than 0.4 of the compression ratio to compress the signal, the mean square error is less than 0.01, prolonging the network life by 2 times.

#### 1. Introduction

There are many compression algorithms in wireless sensor networks such as distributed wavelet compression algorithm [1, 2] (distributed wavelet compression, DWC); it is adopted in the data compression algorithm and made for some changes. DWC compression algorithm has the advantage of good performance and small compression error, but the drawback is the high complexity of the algorithm and the energy cost of calculation is huge, and much communication between the parity nodes will cause wireless sensor node calculation of excessive power consumption and shorten the life of the network. Swinging Door Trending (SDT) [3, 4] has the advantage of a simple algorithm, low energy consumption of calculation, and high calculation speed and can be well applied to the wireless sensor network nodes work, but the disadvantage is that the compression algorithm is relatively small. Because of smaller data changes and slow data changes, SDT in traditional cultural monitoring systems has better performance. But linear compression algorithm performance in cultural intrusion detection process has been greatly affected by the big change in the signal amplitude and fast rate of change.

Compressed sensing theory [5–7] is one of the hotspots in recent years of data and signal processing, widely used in wireless sensor networks. Compressed sensing theory breaking the Nyquist sampling theorem and restriction Shannon theory can be less than the amount of data beyond the classical sampling method to obtain high quality raw response signal. Data reconstruction algorithm is an important part of the process; the key question is how to recover the high-dimensional data from known low-dimensional data in the greatest degree. At present, compressed sensing data reconstruction algorithm includes gradient projection algorithm [8], orthogonal matching algorithm [9], regularization orthogonal matching algorithm [10], tracking based on method [11], and quantum chaos algorithm based on immune clone data reconstruction algorithm Q-CSDR [12].

Current data signal reconstruction algorithm has good performance at low sparsity. Reconstruction conditions, for higher sparsity of signal reconstruction accuracy, algorithm performance plummeted and other problems occur. To solve these problems, the author proposed compression algorithm based on compressed sensing theory of microseismic signals segmentation algorithm by the analysis of data compressed sensing reconstruction algorithm and microseismic signal characteristics. This algorithm is simple segmentation and the complexity of compression algorithm is low, which can significantly improve the signal reconstruction accuracy at high sparsity condition.

#### 2. Algorithms

Sparse data obtained by using linear measurements reconstruct the original information as much as possible to ensure the accuracy of the reconstruction, which is one of the most critical operations of perception frame compression. The reconstruction process of the original signal can be obtained by solving the inverse problem formula (1); then get the original reconstructed signal by the formulaReconstruction of the existing method overall is divided into three categories.

##### 2.1. -Norm Minimization Reconstruction

-norm is actually the least squares program; data reconstruction is the most classic way, with -norm method represented as shown in the formulaTherein, for the vector , -norm is defined as the formulaMinimization reconstruction -norm analytical solution can be easily made as shown in the formulaThis approach theoretically only involves Defy matrix multiplication theory and is very simple, but it cannot be obtained in the calculation process sparse solution; analytical solution obtains more nonzero elements. Therefore, this method is not highly practicable.

##### 2.2. -Norm Minimization Reconstruction

-norm has solved the analytic solution for too many nonzero elements in the -norm minimization problem. In solving the underdetermined linear equations, there are a number of nonzero elements in the minimization. *-norm* is different from the conventional norm with its value equal to the number of nonzero elements; for example, for -sparse signal , its -norm is . So the norm optimization problem is as the formula

In the actual process of reconstruction, it will produce certain error, so formula (5) can also be expressed as the formula

The formula, , is the minimum constant value. To solve this kind of problem, the numerical NP-complete problems are unstable; we need exhaustive solving sparse vector in the position of nonzero elements of possible combinations of kinds.

##### 2.3. -Norm Minimization Reconstruction

Candes pointed out that the met premise conditions are Based on the independent identically distributed Gaussian observation matrix -norm problem can be transformed to the -norm. And using (7) exact reconstruction of sparse signal can be high probability approximation compressible signals:

The application of the above formula will allow the existence of certain errors; the formula is used for solving

The method to solve the -norm minimization is to translate nonconvex problem into a convex programming problem, where solving process is simple. Looking for a minimum of solution space can be expressed as a linear programming problem. But using the -norm for data reconstruction creates the problem of high computational complexity; its computation complexity is .

The existing data of compressed sensing reconstruction algorithms are mostly based on the above three issues. Therein, OMP algorithms are solving the -norm problem, in which core content combines greedy algorithm with iteration method to perceive the column vectors of matrix . Make the selected column vectors and the current residual vectors have the maximum correlation and then subtract the correlated volume from the observable volume and repeat the process until reaching the known sparsity . Q-CSDR algorithm solves the -norm of the problem; in essence, the algorithm is still a greedy algorithm; the core content is to use quantum immune clone algorithm optimization feature; formula (8) is the objective function, using the theory of quantum immediately generated population, using the theory of immune clone population, and constantly looking for the best individual in the population.

#### 3. Microseismic Signal Subsection Compression Algorithm Based on Compressed Sensing

##### 3.1. Microseismic Signal Characteristics and Thinning Methods

Sparsity is the premise condition of compression perception theory; for the data thinned out, we need to first analyze the characteristics of the microseismic data. Sensor for the conventional microseismic data signals is shown in Figure 1.