@InProceedings{8902696,
  author = {A. Bangun and A. Behboodi and R. Mathar},
  booktitle = {2019 27th European Signal Processing Conference (EUSIPCO)},
  title = {Signal Recovery from Phaseless Measurements of Spherical Harmonics Expansion},
  year = {2019},
  pages = {1-5},
  abstract = {In this work, we study the problem of recovering spherical harmonics coefficients from phaseless measurements and evaluate the empirical performance of several well-known algorithms. Apart from trivial ambiguities that arise naturally from the properties of spherical harmonics, we will show that when a specific class of equiangular sampling patterns is chosen to construct the measurement matrix, another ambiguity appears as well. Nevertheless, we will numerically show that recovery can be achieved by carefully choosing the appropriate sampling patterns. Furthermore, an application of this work in phaseless spherical near-field antenna measurements will be addressed.},
  keywords = {matrix algebra;signal sampling;equiangular sampling patterns;measurement matrix;appropriate sampling patterns;phaseless spherical near-field antenna measurements;signal recovery;phaseless measurements;spherical harmonics expansion;spherical harmonics coefficients;empirical performance;trivial ambiguities;Harmonic analysis;Phase measurement;Antenna measurements;Signal processing algorithms;Europe;Optical variables measurement;Phase retrieval;spherical harmonics;spherical near-field measurements},
  doi = {10.23919/EUSIPCO.2019.8902696},
  issn = {2076-1465},
  month = {Sep.},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2019/proceedings/papers/1570534145.pdf},
}

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Apart from trivial ambiguities that arise naturally from the properties of spherical harmonics, we will show that when a specific class of equiangular sampling patterns is chosen to construct the measurement matrix, another ambiguity appears as well. Nevertheless, we will numerically show that recovery can be achieved by carefully choosing the appropriate sampling patterns. 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