Spatio-Temporal Signal Recovery Based on Low Rank and Differential Smoothness

The analysis of spatio-temporal signals plays an important role in various fields including sociology, climatology, and environmental studies, etc. Due to the abrupt breakdown of the sensors in the sensor network, there always are missing entries in the observed spatio-temporal signals. In this paper, we study the problem of recovering spatio-temporal signals from partially known entries. Based on both the global and local correlated property of spatio-temporal signals, we propose a low rank and differential smoothness based recovery method (LRDS), which novelly introduces the differential smooth prior of time-varying graph signals to the field of spatio-temporal signal analysis. The performance of the proposed method is analyzed theoretically. Considering the case where a priori information about the signal's global pattern is available, we propose prior LRDS to further improve the reconstruction accuracy. Such improvement is also verified by synthetic experiments. Besides, experiments on several real-world datasets demonstrate the improvement on recovery accuracy of the proposed LRDS over the state-of-the-art spatio-temporal signal recovery methods.

[1]  B. Mercier,et al.  A dual algorithm for the solution of nonlinear variational problems via finite element approximation , 1976 .

[2]  Jonathan Eckstein,et al.  Understanding the Convergence of the Alternating Direction Method of Multipliers: Theoretical and Computational Perspectives , 2015 .

[3]  Santiago Segarra,et al.  Sampling of Graph Signals With Successive Local Aggregations , 2015, IEEE Transactions on Signal Processing.

[4]  Dehui Yang,et al.  Weighted Matrix Completion and Recovery With Prior Subspace Information , 2018, IEEE Transactions on Information Theory.

[5]  Jelena Kovacevic,et al.  Discrete Signal Processing on Graphs: Sampling Theory , 2015, IEEE Transactions on Signal Processing.

[6]  José M. F. Moura,et al.  Discrete Signal Processing on Graphs , 2012, IEEE Transactions on Signal Processing.

[7]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2009, Found. Comput. Math..

[8]  Philipp Birken,et al.  Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.

[9]  Xue Liu,et al.  Data loss and reconstruction in sensor networks , 2013, 2013 Proceedings IEEE INFOCOM.

[10]  Johan Lindström,et al.  Reduced-Rank Spatio-Temporal Modeling of Air Pollution Concentrations in the Multi-Ethnic Study of Atherosclerosis and Air Pollution. , 2014, The annals of applied statistics.

[11]  I. Pesenson.  Sampling in paley-wiener spaces on combinatorial graphs , 2008, 1111.5896.

[12]  Noel A Cressie,et al.  Statistics for Spatio-Temporal Data , 2011 .

[13]  Junbin Gao,et al.  Correlated Spatio-Temporal Data Collection in Wireless Sensor Networks Based on Low Rank Matrix Approximation and Optimized Node Sampling , 2014, Sensors.

[14]  Yanfeng Sun,et al.  Efficient Data Gathering in Wireless Sensor Networks Based on Low Rank Approximation , 2013, 2013 IEEE International Conference on Green Computing and Communications and IEEE Internet of Things and IEEE Cyber, Physical and Social Computing.

[15]  Yuantao Gu,et al.  A Distributed Tracking Algorithm for Reconstruction of Graph Signals , 2015, IEEE Journal of Selected Topics in Signal Processing.

[16]  H. E. Bell,et al.  Gershgorin's Theorem and the Zeros of Polynomials , 1965 .

[17]  Michael B. Wakin,et al.  MC^2: A Two-Phase Algorithm for Leveraged Matrix Completion , 2016, ArXiv.

[18]  Qiang Ye,et al.  STCDG: An Efficient Data Gathering Algorithm Based on Matrix Completion for Wireless Sensor Networks , 2013, IEEE Transactions on Wireless Communications.

[19]  Mark A. Anastasio,et al.  Low-rank matrix estimation-based spatio-temporal image reconstruction for dynamic photoacoustic computed tomography , 2014, Photonics West - Biomedical Optics.

[20]  Lei Yao,et al.  A DCT Regularized Matrix Completion Algorithm for Energy Efficient Data Gathering in Wireless Sensor Networks , 2015, Int. J. Distributed Sens. Networks.

[21]  Ali M. Mosammam,et al.  Estimation and testing for covariance-spectral spatial-temporal models , 2014, Environmental and Ecological Statistics.

[22]  Cagdas Ulas,et al.  Spatio-temporal MRI reconstruction by enforcing local and global regularity via dynamic total variation and nuclear norm minimization , 2016, 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI).

[23]  W. Hackbusch.  Iterative Solution of Large Sparse Systems of Equations , 1993 .

[24]  José M. F. Moura,et al.  Signal Recovery on Graphs: Variation Minimization , 2014, IEEE Transactions on Signal Processing.

[25]  Mohammed E. El-Telbany,et al.  Exploiting Sparsity in Wireless Sensor Networks for Energy Saving : A Comparative Study , 2017 .

[26]  Stephen P. Boyd,et al.  Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers , 2011, Found. Trends Mach. Learn..

[27]  Yuantao Gu,et al.  Local measurement and reconstruction for noisy bandlimited graph signals , 2016, Signal Process..

[28]  Pengfei Liu,et al.  Coarsening graph signal with spectral invariance , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[29]  Yuantao Gu,et al.  Time-Varying Graph Signal Reconstruction , 2017, IEEE Journal of Selected Topics in Signal Processing.

[30]  Yan Liu.  Scalable Multivariate Time-Series Models for Climate Informatics , 2015, Computing in Science & Engineering.

[31]  Antonio Ortega,et al.  Graph Learning from Data under Structural and Laplacian Constraints , 2016, ArXiv.

[32]  Michael Gertz,et al.  A probablistic model for spatio-temporal signal extraction from social media , 2013, SIGSPATIAL/GIS.

[33]  Alba Pagès-Zamora,et al.  Matrix completion of noisy graph signals via proximal gradient minimization , 2017, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[34]  Haiying Wang.  Principal Component Analysis on Temporal-spatial Variations of Sea Level Anomalies from T/P Satellite Altimeter Data over the Northwest Pacific , 2001 .

[35]  Alexander S. Szalay,et al.  Data Management in the Worldwide Sensor Web , 2007, IEEE Pervasive Computing.

[36]  Pengfei Liu,et al.  Local-Set-Based Graph Signal Reconstruction , 2014, IEEE Transactions on Signal Processing.

[37]  Thomas M. Smith,et al.  Improved Extended Reconstruction of SST (1854–1997) , 2004 .

[38]  Walter Willinger,et al.  Spatio-temporal compressive sensing and internet traffic matrices , 2009, SIGCOMM '09.

[39]  Robert D. Nowak,et al.  Socioscope: Spatio-Temporal Signal Recovery from Social Media (Extended Abstract) , 2012, IJCAI.

[40]  Junzhou Huang,et al.  A spatio-temporal low-rank total variation approach for denoising arterial spin labeling MRI data , 2015, 2015 IEEE 12th International Symposium on Biomedical Imaging (ISBI).

[41]  Pascal Frossard,et al.  The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains , 2012, IEEE Signal Processing Magazine.

[42]  Shiqian Ma,et al.  Fixed point and Bregman iterative methods for matrix rank minimization , 2009, Math. Program..

[43]  Santiago Segarra,et al.  Network topology identification from spectral templates , 2016, 2016 IEEE Statistical Signal Processing Workshop (SSP).

[44]  Qi Yu,et al.  Fast Multivariate Spatio-temporal Analysis via Low Rank Tensor Learning , 2014, NIPS.

[45]  Feiping Nie,et al.  Low-Rank Tensor Completion with Spatio-Temporal Consistency , 2014, AAAI.