Signal inpainting on graphs via total variation minimization

We propose a novel recovery algorithm for signals with complex, irregular structure that is commonly represented by graphs. Our approach is a generalization of the signal inpainting technique from classical signal processing. We formulate corresponding minimization problems and demonstrate that in many cases they have closed-form solutions. We discuss a relation of the proposed approach to regression, provide an upper bound on the error for our algorithm and compare the proposed technique with other existing algorithms on real-world datasets.

[1]  Hae Young Noh,et al.  Damage quantification and localization algorithms for indirect SHM of bridges , 2014 .

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

[3]  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.

[4]  Joel B. Harley,et al.  Multiresolution classification with semi-supervised learning for indirect bridge structural health monitoring , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[5]  José M. F. Moura,et al.  Discrete Signal Processing on Graphs: Frequency Analysis , 2013, IEEE Transactions on Signal Processing.

[6]  Mikhail Belkin,et al.  Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples , 2006, J. Mach. Learn. Res..

[7]  James H. Garrett,et al.  Indirect structural health monitoring of a simplified laboratory-scale bridge model , 2014 .

[8]  James H. Garrett,et al.  Semi-Supervised Multiresolution Classification Using Adaptive Graph Filtering With Application to Indirect Bridge Structural Health Monitoring , 2014, IEEE Transactions on Signal Processing.

[9]  Zoubin Ghahramani,et al.  Combining active learning and semi-supervised learning using Gaussian fields and harmonic functions , 2003, ICML 2003.

[10]  José M. F. Moura,et al.  Adaptive graph filtering: Multiresolution classification on graphs , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[11]  Lada A. Adamic,et al.  The political blogosphere and the 2004 U.S. election: divided they blog , 2005, LinkKDD '05.

[12]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[13]  Tony F. Chan,et al.  The digital TV filter and nonlinear denoising , 2001, IEEE Trans. Image Process..

[14]  Pierre Vandergheynst,et al.  Wavelets on Graphs via Spectral Graph Theory , 2009, ArXiv.

[15]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[16]  B. Schölkopf,et al.  A Regularization Framework for Learning from Graph Data , 2004, ICML 2004.

[17]  James H. Garrett,et al.  Indirect structural health monitoring in bridges: scale experiments , 2012 .

[18]  ANTONIN CHAMBOLLE,et al.  An Algorithm for Total Variation Minimization and Applications , 2004, Journal of Mathematical Imaging and Vision.