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Hypercomplex algebras for dictionary learning

Srdan Lazendic (UGent) , Aleksandra Pizurica (UGent) and Hendrik De Bie (UGent)
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Abstract
This paper presents an application of hypercomplex algebras combined with dictionary learning for sparse representation of multichannel images. Two main representatives of hypercomplex algebras, Clifford algebras and algebras generated by the Cayley-Dickson procedure are considered. Related works reported quaternion methods (for color images) and octonion methods, which are applicable to images with up to 7 channels. We show that the current constructions cannot be generalized to dimensions above eight.
Keywords
Hypercomplex algebras, Clifford algebras, Cayley-Dickson algebras, Quaternions, Octonions, Image Processing, Dictionary Learning

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Please use this url to cite or link to this publication:

MLA
Lazendic, Srdan, et al. “Hypercomplex Algebras for Dictionary Learning.” Early Proceedings of the AGACSE 2018 Conference, Unicamp/IMECC, 2018, pp. 57–64.
APA
Lazendic, S., Pizurica, A., & De Bie, H. (2018). Hypercomplex algebras for dictionary learning. In Early Proceedings of the AGACSE 2018 Conference (pp. 57–64). Campinas, Brazil: Unicamp/IMECC.
Chicago author-date
Lazendic, Srdan, Aleksandra Pizurica, and Hendrik De Bie. 2018. “Hypercomplex Algebras for Dictionary Learning.” In Early Proceedings of the AGACSE 2018 Conference, 57–64. Campinas, Brazil: Unicamp/IMECC.
Chicago author-date (all authors)
Lazendic, Srdan, Aleksandra Pizurica, and Hendrik De Bie. 2018. “Hypercomplex Algebras for Dictionary Learning.” In Early Proceedings of the AGACSE 2018 Conference, 57–64. Campinas, Brazil: Unicamp/IMECC.
Vancouver
1.
Lazendic S, Pizurica A, De Bie H. Hypercomplex algebras for dictionary learning. In: Early Proceedings of the AGACSE 2018 Conference. Campinas, Brazil: Unicamp/IMECC; 2018. p. 57–64.
IEEE
[1]
S. Lazendic, A. Pizurica, and H. De Bie, “Hypercomplex algebras for dictionary learning,” in Early Proceedings of the AGACSE 2018 Conference, Campinas, São Paulo, Brazil, 2018, pp. 57–64.
@inproceedings{8570237,
  abstract     = {This paper presents an application of hypercomplex algebras combined with dictionary learning for sparse representation of multichannel images. Two main representatives of hypercomplex algebras, Clifford algebras and algebras generated by the Cayley-Dickson procedure are considered. Related works reported quaternion methods (for color images) and octonion methods, which are applicable to images with up to 7 channels. We show that the current constructions cannot be generalized to dimensions above eight.},
  author       = {Lazendic, Srdan and Pizurica, Aleksandra and De Bie, Hendrik},
  booktitle    = {Early Proceedings of the AGACSE 2018 Conference},
  isbn         = {978‐84‐9880‐703‐5},
  keywords     = {Hypercomplex algebras,Clifford algebras,Cayley-Dickson algebras,Quaternions,Octonions,Image Processing,Dictionary Learning},
  language     = {eng},
  location     = {Campinas, São Paulo, Brazil},
  pages        = {57--64},
  publisher    = {Unicamp/IMECC},
  title        = {Hypercomplex algebras for dictionary learning},
  year         = {2018},
}