Update: Papers from SampTA and SPARS

SampTA 2013 and SPARS 2013 are back to back (almost) next to each other and I am fortunate to participate in both. They are very interesting events and always gather a great group of people.

This year I am presenting work on measuring and recovering sparse signals using phase measurements. In both papers [1, 2] , we obtain linear measurements of real signals using a complex measurement matrix and only record the phase of those measurements. This can be considered as an extension of 1-bis CS [3, 4] since the phase of a complex number generalizes the sign of a real number.

The SPARS paper  [1] discusses how such measurements implement embeddings that preserve angles (i.e., correlations) between signals. The SamTA paper [2] further shows that we can in fact reconstruct from such measurements. Although the theory is not all the way there yet, in practice we observe exact reconstruction patterns, similar to classical CS. These results are very exciting and promising!

[1]

P. T. Boufounos, “On Embedding The Angles Between Signals,” Proc. Signal Processing with Adaptive Sparse Structured Representations (SPARS), Lausanne, Switzerland, July 8-11, 2013.

[preprint] [Bibtex]

@inproceedings{B_SPARS13,
  Address =   {Lausanne, Switzerland},
  Author =   {Boufounos, P. T.},
  Booktitle =   {Proc. Signal Processing with Adaptive Sparse Structured Representations (SPARS)},
  Month =   {July 8-11},
  Url =     {http://spars2013.epfl.ch/data/_uploaded/flash/Paper%2058.pdf},
  Pdf =     {http://boufounos.com/Publications/B_SPARS2013.pdf},
  Title =   {On Embedding The Angles Between Signals},
  Year =   {2013}
}

[2]

P. T. Boufounos, “Sparse Signal Reconstruction from Phase-only Measurements,” Proc. Int. Conf. Sampling Theory and Applications (SampTA), Bremen, Germany, July 1-5, 2013.

[preprint] [Bibtex]

@inproceedings{B_SampTA13,
  Address =   {Bremen, Germany},
  Author =   {Boufounos, P. T.},
  Booktitle =   {Proc. Int. Conf. Sampling Theory and Applications (SampTA)},
  Month =   {July 1-5},
  Pdf =     {http://boufounos.com/Publications/B_SampTA2013.pdf},
  Title =   {Sparse Signal Reconstruction from Phase-only Measurements},
  Year =   {2013}
}

[3]

P. T. Boufounos and R. G. Baraniuk, “1-Bit Compressive Sensing,” Proc. Conf. Inform. Science and Systems (CISS), Princeton, NJ, March 19-21, 2008.

[preprint] [Bibtex]

@inproceedings{BB_CISS08,
  Address =   {Princeton, NJ},
  Author =   {Boufounos, P. T. and Baraniuk, R. G.},
  Booktitle =   {Proc. Conf. Inform. Science and Systems (CISS)},
  Doi =     {10.1109/CISS.2008.4558487},
  Month =   {March 19-21},
  Pdf =     {http://boufounos.com/Publications/Boufounos_Baraniuk_CISS08.pdf},
  Title =   {1-Bit Compressive Sensing},
  Url =     {http://dx.doi.org/10.1109/CISS.2008.4558487},
  Year =   {2008}
}

[4]

L. Jacques, J. N. Laska, P. T. Boufounos, and R. G. Baraniuk, “Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors,” IEEE Trans. Info. Theory, v. 59, no. 4, April, 2013.

[preprint] [arXiv] [Bibtex]

@article{JLBB_TIT13,
  Arxivurl =   {http://arxiv.org/abs/1104.3160},
  Author =   {Jacques, L. and Laska, J. N. and Boufounos, P. T. and Baraniuk, R. G.},
  Journal =   {IEEE Trans. Info. Theory},
  Pdf =     {http://boufounos.com/Publications/JLBB_BSE.pdf},
  Title =   {Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors},
  Url =     {http://dx.doi.org/10.1109/TIT.2012.2234823},
  Doi =     {10.1109/TIT.2012.2234823},
  volume =   {59},
  number =   {4},
  Month =   {April},
  Year =   {2013}
}