Iterative methods for signal reconstruction on graphs

We present two iterative algorithms to interpolate graph signals from only a partial set of samples. Our methods are derived from classical iterative schemes in presence of irregular samples and compared with existing graph signal reconstruction algorithms in order to study the rate of convergence and the computational efficiency. The experimental results demonstrate the effectiveness of the proposed methods.

[1]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

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

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

[4]  Paulo Jorge S. G. Ferreira.  Interpolation and the discrete Papoulis-Gerchberg algorithm , 1994, IEEE Trans. Signal Process..

[5]  Sergio Barbarossa,et al.  Signals on Graphs: Uncertainty Principle and Sampling , 2015, IEEE Transactions on Signal Processing.

[6]  O. Christensen.  An introduction to frames and Riesz bases , 2002 .

[7]  Jose M. F. Moura,et al.  Representation and processing of massive data sets with irregular structure ] Big Data Analysis with Signal Processing on Graphs , 2022 .

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

[9]  Farrokh Marvasti,et al.  Recovery of signals from nonuniform samples using iterative methods , 1991, IEEE Trans. Signal Process..

[10]  V. Berinde.  Iterative Approximation of Fixed Points , 2007 .

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

[12]  Santiago Segarra,et al.  Reconstruction of Graph Signals Through Percolation from Seeding Nodes , 2015, IEEE Transactions on Signal Processing.

[13]  R. Gerchberg.  Super-resolution through Error Energy Reduction , 1974 .

[14]  Sunil K. Narang,et al.  Localized iterative methods for interpolation in graph structured data , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[15]  Bernhard Schölkopf,et al.  Learning from Labeled and Unlabeled Data Using Random Walks , 2004, DAGM-Symposium.

[16]  W. R. Mann,et al.  Mean value methods in iteration , 1953 .

[17]  Michael G. Rabbat,et al.  Approximating signals supported on graphs , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[18]  K. Gröchenig.  A discrete theory of irregular sampling , 1993 .

[19]  Hans G. Feichtinger,et al.  Theory and practice of irregular sampling , 2021, Wavelets.

[20]  S. L. Joshi,et al.  A Survey on ECG Signal Denoising Techniques , 2013, 2013 International Conference on Communication Systems and Network Technologies.

[21]  C. E. Chidume,et al.  Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappings , 1987 .

[22]  Antonio Ortega,et al.  Submitted to Ieee Transactions on Signal Processing 1 Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies , 2022 .

[23]  Noah E. Friedkin,et al.  Theoretical Foundations for Centrality Measures , 1991, American Journal of Sociology.

[24]  F. Marvasti.  Nonuniform sampling : theory and practice , 2001 .

[25]  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.

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

[27]  K. Gröchenig.  RECONSTRUCTION ALGORITHMS IN IRREGULAR SAMPLING , 1992 .

[28]  A. Papoulis.  A new algorithm in spectral analysis and band-limited extrapolation. , 1975 .

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

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

[31]  Sunil K. Narang,et al.  Signal processing techniques for interpolation in graph structured data , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[32]  Giuseppe De Pietro,et al.  A revised scheme for real time ECG Signal denoising based on recursive filtering , 2016, Biomed. Signal Process. Control..