The Research About Methods Of Gravimetry Data Reconstruction Based On Compressed Sensing

In recent years, with the rapid development of gravimetry technology and the wide application of Earth’s gravity field information, the gravity data reconstructed by conventional interpolation method based on the numerical approximation problem, have been unable to meet the needs of scientific research and engineering practice on the data accuracy, spatial resolution and computational efficiency. So it is becoming more and more urgent that exploring the new high accuracy and high resolution methods on gravity data reconstruction.With the research background of measuring the Earth’s gravity and building the Earth’s gravity field model, the paper mainly studied the new gravity data reconstruction method based on the theory of compressed sensing. Combining the three key technologies of compressed sensing, we studied the sparsity of gravity data in the Fourier transform domain, Wavelet transform domain and Curvelet transform domain, analysed the compressed sampling method for gravity data reconstruction with high precision, and proposed a variety of gravity data reconstruction algorithms with high efficiency and high accuracy. The main results are summarized as follows:(1) We deeply analysed the basic principles and implementation methods of the Fourier transform, Wavelet transform and Curvelet transform, proposed the sparsity analysis of one-dimensional gravimetry data using the discrete Fourier transform. And using airborne gravimetry data, we verified the effectiveness of sparse representation methods based on discrete Fourier transform. Meanwhile, we proposed the sparsity analysis of two-dimensional gravimetry data using discrete Wavelet transform and fast discrete Curvelet transform. And we verified the feasibility of above sparse representation methods by the EGM2008 model gravity data and observed gravity data.(2) For the method of constructing the compressed sampling matrix of gravity data, we deeply studied of the impact of reconstruction accuracy with the totally random sampling method and piecewise random sampling approach. The results showed that piecewise random sampling method not only ensured the sample gravity data not be too close and more uniform distribution, but also allowed the compressed sampling matrix remain fairly random. So the piecewise random sampling approach is an ideal and practical sampling method. All the sparse reconstruction algorithms proposed in the following chapters were based on the piecewise random sampling approach.(3) Based on the one-dimensional gravity data is sparse in the discrete Fourier transform domain, the paper presented the gravity data reconstruction was transformed into the L0 norm sparse optimization problem, and introduced the orthogonal matching pursuit algorithm to solve this problem. The gravity anomaly data of six survey lines in the airborne gravimetry flight test F402 were reconstructed. The results showed that Orthogonal Matching Pursuit algorithm can reconstruct the gravity data with sample rate of 35%, the standard deviation of reconstruction error was better than 0.03 m Gal, and the signal to noise ratio was better than 58 d B. The overall performance evaluation of this algorithm was superior to the commonly used spline interpolation method.(4) Based on Compressed Sensing, the gravity data reconstruction was transformed into the L1 norm convex quadratic programming. Combined with preconditioned conjugate gradient algorithm, the paper presented an improved interior point method to achieve the large-scale gravity data reconstruction. Based on the gravity data reconstruction experiment of six survey lines in the airborne gravimetry flight test F401 and F405, the improved interior point method’s calculation speed was faster with high accuracy, compared with the traditional interior point and spline interpolation method. But the sample rate is 45% and more than the Orthogonal Matching Pursuit algorithm.(5) Based on the two-dimensional gravity data is sparse in discrete Wavelet transform domain, the paper extended orthogonal matching pursuit algorithm to reconstruct the two-dimensional gravity data. Based on the reconstruction experiment of EGM2008 model gravity data and observed gravity data, the Extended Orthogonal Matching Pursuit algorithm effectively solved the two-dimensional gravity data reconstruction, the sampling rate was 50%, and the standard deviation of reconstruction error was lower than 0.7 m Gal. The overall performance evaluation of Extended Orthogonal Matching Pursuit algorithm was better than the spline interpolation method.(6) Based on the two-dimensional gravity data is sparse in fast discrete Curvelet transform domain, the paper transformed the gravity data reconstruction into the L1 norm basis pursuit denoise problem and introduced the spectral projected gradient algorithm to solve this problem. Based on the reconstruction experiment of EGM2008 model gravity data and observed gravity data, the spectral projected gradient algorithm effectively solved the two-dimensional gravity data reconstruction, the sampling rate was 50%, the standard deviation of reconstruction error was lower than 0.5m Gal, and the signal to noise ratio was greater than 30 d B. The performance evaluation of spectral projected gradient algorithm was better than the spline interpolation method and Extended Orthogonal Matching Pursuit algorithm.