In this paper, a high-dimensional statistical signal processing is revisited with the aim of introducing the concept of vector signal representation derived from the Riesz transforms, which are the natural extension and generalization of the one-dimensional Hilbert transform. Under the new concepts of vector correlations proposed recently, the statistical properties of the vector signal representation for random signal are presented and some applications to speckle metrology developed recently are reviewed to demonstrate the unique capability of Riesz transforms.
|Title of host publication||Proceedings of SPIE|
|Number of pages||9|
|Publisher||SPIE - International Society for Optical Engineering|
|Publication status||Published - 2015|
|Event||International Conference on Photonics and Optical Engineering - Xi'an, China|
Duration: 13 Oct 2014 → 15 Oct 2014
|Conference||International Conference on Photonics and Optical Engineering|
|Period||13/10/2014 → 15/10/2014|
|Series||Proceedings of SPIE, the International Society for Optical Engineering|
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Wang, W., Zhang, S., Ma, N., Hanson, S. G., & Takeda, M. (2015). Riesz transforms in statistical signal processing and their applications to speckle metrology: a review. In Proceedings of SPIE (Vol. 9449).  SPIE - International Society for Optical Engineering. Proceedings of SPIE, the International Society for Optical Engineering, Vol.. 9449 https://doi.org/10.1117/12.2081318