
Update: Papers from SampTA and SPARS By PetrosB, on July 1st, 2013 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 1bis 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 811, 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 811},
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 Phaseonly Measurements,” Proc. Int. Conf. Sampling Theory and Applications (SampTA), Bremen, Germany, July 15, 2013.
[preprint] [Bibtex]
@inproceedings{B_SampTA13,
Address = {Bremen, Germany},
Author = {Boufounos, P. T.},
Booktitle = {Proc. Int. Conf. Sampling Theory and Applications (SampTA)},
Month = {July 15},
Pdf = {http://boufounos.com/Publications/B_SampTA2013.pdf},
Title = {Sparse Signal Reconstruction from Phaseonly Measurements},
Year = {2013}
}

[3] 
P. T. Boufounos and R. G. Baraniuk, “1Bit Compressive Sensing,” Proc. Conf. Inform. Science and Systems (CISS), Princeton, NJ, March 1921, 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 1921},
Pdf = {http://boufounos.com/Publications/Boufounos_Baraniuk_CISS08.pdf},
Title = {1Bit 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 1Bit 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 1Bit 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}
}


