Blind Identification of Invertible Graph Filters with Multiple Sparse Inputs. Ye, C., Shafipour, R., & Mateos, G. In 2018 26th European Signal Processing Conference (EUSIPCO), pages 121-125, Sep., 2018.
Blind Identification of Invertible Graph Filters with Multiple Sparse Inputs [pdf]Paper  doi  abstract   bibtex   
This paper deals with the problem of blind identification of a graph filter and its sparse input signal, thus broadening the scope of classical blind deconvolution of temporal and spatial signals to irregular graph domains. While the observations are bilinear functions of the unknowns, a mild requirement on invertibility of the filter enables an efficient convex formulation, without relying on matrix lifting that can hinder applicability to large graphs. On top of scaling, it is argued that (non-cyclic) permutation ambiguities may arise with some particular graphs. Deterministic sufficient conditions under which the proposed convex relaxation can exactly recover the unknowns are stated, along with those guaranteeing identifiability under the Bernoulli-Gaussian model for the inputs. Numerical tests with synthetic and real-world networks illustrate the merits of the proposed algorithm, as well as the benefits of leveraging multiple signals to aid the (blind) localization of sources of diffusion.
@InProceedings{8553229,
  author = {C. Ye and R. Shafipour and G. Mateos},
  booktitle = {2018 26th European Signal Processing Conference (EUSIPCO)},
  title = {Blind Identification of Invertible Graph Filters with Multiple Sparse Inputs},
  year = {2018},
  pages = {121-125},
  abstract = {This paper deals with the problem of blind identification of a graph filter and its sparse input signal, thus broadening the scope of classical blind deconvolution of temporal and spatial signals to irregular graph domains. While the observations are bilinear functions of the unknowns, a mild requirement on invertibility of the filter enables an efficient convex formulation, without relying on matrix lifting that can hinder applicability to large graphs. On top of scaling, it is argued that (non-cyclic) permutation ambiguities may arise with some particular graphs. Deterministic sufficient conditions under which the proposed convex relaxation can exactly recover the unknowns are stated, along with those guaranteeing identifiability under the Bernoulli-Gaussian model for the inputs. Numerical tests with synthetic and real-world networks illustrate the merits of the proposed algorithm, as well as the benefits of leveraging multiple signals to aid the (blind) localization of sources of diffusion.},
  keywords = {blind source separation;convex programming;deconvolution;filtering theory;Gaussian processes;graph theory;matrix algebra;multiple sparse inputs;blind identification;graph filter;sparse input signal;temporal signals;spatial signals;bilinear functions;convex relaxation;invertible graph filters;blind deconvolution;convex formulation;Bernoulli-Gaussian model;Signal processing;Deconvolution;Mathematical model;Signal processing algorithms;Sparse matrices;Minimization;Graph signal processing;network diffusion;bilinear equations;blind deconvolution;convex optimization},
  doi = {10.23919/EUSIPCO.2018.8553229},
  issn = {2076-1465},
  month = {Sep.},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2018/papers/1570439437.pdf},
}
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