Compressed sensing data reconstruction using a modified subspace pursuit algorithm under the condition of unknown sparsity

Irregular sampled gravity data are often interpolated into regular grid data for convenience of data processing and interpretation. The compressed sensing theory provides a signal reconstruction method that can recover a sparse signal from far fewer samples. We have introduced a gravity data reconstruction method based on the nonequispaced Fourier transform (NFT) in the framework of compressed sensing theory. We have developed a sparsity analysis and a reconstruction algorithm with an iterative cooling thresholding method and applied to the gravity data of the Bishop model. For 2D data reconstruction, we use two methods to build the weighting factors: the Gaussian function and the Voronoi method. Both have good reconstruction results from the 2D data tests. The 2D reconstruction tests from different sampling rates and comparison with the minimum curvature and the kriging methods indicate that the reconstruction method based on the NFT has a good reconstruction result even with few sampling data.

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Application-driven sensing data reconstruction and selection based on correlation mining and dynamic feedback

2016 IEEE International Conference on Big Data (Big Data) ◽

10.1109/bigdata.2016.7840737 ◽

2016 ◽

Cited By ~ 3

Author(s):

Zhichuan Huang ◽

Tiantian Xie ◽

Ting Zhu ◽

Jianwu Wang ◽

Qingquan Zhang

Keyword(s):

Data Reconstruction ◽

Dynamic Feedback ◽

Sensing Data ◽

Correlation Mining

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Compressive-sensing data reconstruction for structural health monitoring: a machine-learning approach

Structural Health Monitoring ◽

10.1177/1475921719844039 ◽

2019 ◽

Vol 19 (1) ◽

pp. 293-304 ◽

Cited By ~ 7

Author(s):

Yuequan Bao ◽

Zhiyi Tang ◽

Hui Li

Keyword(s):

Machine Learning ◽

Structural Health Monitoring ◽

Compressive Sensing ◽

Health Monitoring ◽

Applied Mathematics ◽

Modal Identification ◽

Data Reconstruction ◽

Wireless Data ◽

Sensing Data ◽

Structural Health

Compressive sensing has been studied and applied in structural health monitoring for data acquisition and reconstruction, wireless data transmission, structural modal identification, and spare damage identification. The key issue in compressive sensing is finding the optimal solution for sparse optimization. In the past several years, many algorithms have been proposed in the field of applied mathematics. In this article, we propose a machine learning–based approach to solve the compressive-sensing data-reconstruction problem. By treating a computation process as a data flow, the solving process of compressive sensing–based data reconstruction is formalized into a standard supervised-learning task. The prior knowledge, i.e. the basis matrix and the compressive sensing–sampled signals, is used as the input and the target of the network; the basis coefficient matrix is embedded as the parameters of a certain layer; and the objective function of conventional compressive sensing is set as the loss function of the network. Regularized by l1-norm, these basis coefficients are optimized to reduce the error between the original compressive sensing–sampled signals and the masked reconstructed signals with a common optimization algorithm. In addition, the proposed network is able to handle complex bases, such as a Fourier basis. Benefiting from the nature of a multi-neuron layer, multiple signal channels can be reconstructed simultaneously. Meanwhile, the disassembled use of a large-scale basis makes the method memory-efficient. A numerical example of multiple sinusoidal waves and an example of field-test wireless data from a suspension bridge are carried out to illustrate the data-reconstruction ability of the proposed approach. The results show that high reconstruction accuracy can be obtained by the machine learning–based approach. In addition, the parameters of the network have clear meanings; the inference of the mapping between input and output is fully transparent, making the compressive-sensing data-reconstruction neural network interpretable.

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