Compressed Sensing to Power Quality Signal with Orthogonal Matching Pursuit Method

Compressed sensing is a new data compression method which can recover a sparse or compressible signal from a small number of linear and non-adaptive measurements. To solve the problems of high sampling rate and massive data storage faced by traditional collection and compression methods of power quality, compressed sensing algorithm is used in the paper. Gaussian random measurement matrix is used to complete the compressed sampling. The orthogonal matching pursuit method is adopted in the reconstruction processes. Simulation show that The SNR of the reconstruction of harmonics signal using compressed sensing is higher than the traditional compression method such as wavelet transform and DCT transform. I.Introduction Data acquisition method is one of the key theories and techniques of power quality monitoring system. Traditional methods for acquisition and compression of power quality signals are based on Nyquist sampling theory, which are faced with such troubles as high sampling rate, waste of sampling resources and high attainable cost for hardware. To solve these problems, based on compressed sensing (CS) theory a method for compressed sampling and reconstruction of power quality data is introduced here. Different from the traditional signal acquisition process, compressed sensing, which is a new theory that captures and represents compressible signals at a sampling rate significantly below the Nyquist rate. It first employs non-adaptive linear projections that preserve the structure of the signal, and then the signal reconstruction is conducted using an optimization process from these projections. Compressed sensing has been a research hotspot and a new theoretical framework in the field of signal processing . Three problems would to be solved: (1) Signal sparse representation. (2) Design of measurement matrix. (3) Reconstruction algorithm matching with sparse decomposition. II. Problem formulation The basic topic of compressed sensing is to determine the minimal number n of linear nonadaptive measurement that allows for reconstruction of a signal N x R ∈ that has at most k nonzero components. A. Sparse representation. From Fourier transform to wavelet transform, scientists have devoted themselves to find a simple and effective representation of different kind of signal in function space. The object of these transforms is to exploring the sparse of signal, or to enhancing the approximation ability of signal to non-linear function. The theories of compressed sensing think that signal has a very sparse representation in the time domain, or in an orthonormal basis or redundant dictionary, according to that the natural signals and images are significantly sparse in frequency domain. The definition of sparsity is proposed by Donoho in [4]: the transform coefficients of signal x in orthogonal basis {Y} is Θ=ΨX. Let 0<p<2 and R>0, if those coefficients satisfy: 1/ || || ( | | ) p p p i i R θ Θ ≡ ≤ ∑ (1) 4th International Conference on Machinery, Materials and Information Technology Applications (ICMMITA 2016) Copyright © 2017, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Computer Science Research, volume 71