Sparse Approximations for Quaternionic Signals

Advances in Applied Clifford Algebras

Volumn 24, Issue 2, 2014, Pages 383-402

  Barthélemy, Quentin ^a   Larue, Anthony ^a   Mars, Jérôme I ^b  

^a DIF   (France)

^b GIPSA LAB   (France)

Author keywords

orthogonal matching pursuit; Quaternionic signal processing; sparse approximation

Indexed keywords

EID: 84893389662     PISSN: 01887009     EISSN: 16614909     Source Type: Journal    
DOI: 10.1007/s00006-013-0437-x     Document Type: Article

References (18)

1. B. Augereau and P. Carré, Hypercomplex polynomial wavelet packet application for color image. In Conf. on Applied Geometric Algebras in Computer Science and Engineering AGACSE, 2012.
2. Q. Barthelemy, A. Larue and J. I. Mars, Quaternionic sparse approximation. In Conf. on Applied Geometric Algebras in Computer Science and Engineering AGACSE, 2012.
3. Q. Barthelemy, A. Larue, A. Mayoue, D. Mercier and J. I. Mars, Shift & 2D rotation invariant sparse coding for multivariate signals. IEEE Trans. on Signal Processing, 60 (2012), 15971611.
4. D. H. Brandwood, A complex gradient operator and its application in adaptive array theory. IEE Proceedings F - Communications, Radar and Signal Processing 130 (1983), 1116.
5. Chan W. L., Choi H., Baraniuk R. G.: Coherent multiscale image processing using dual-tree quaternion wavelets. IEEE Trans. on Image Processing 17, 10691082 (2008).
6. Cotter S. F., Adler R., Rao R. D., Kreutz-Delgado K.: Forward sequential algorithms for best basis selection. IEE Proceedings - Vision, Image and Signal Processing 146, 235244 (1999).
7. Davis G., Mallat S., Zhang Z.: time-frequency decompositions with matching pursuits. Optical Engineering, 33, 21832191 (1994).
8. A. J. Hanson, Visualizing quaternion. Morgan-Kaufmann/Elsevier, 2006.
9. S. Javidi, C. C. Took, C. Jahanchahi, N. Le Bihan and D. P. Mandic, Blind extraction of improper quaternion sources. In Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing ICASSP 11, (2011), pages 37083711.
10. N. Le Bihan and J. Mars, Singular value decomposition of quaternion matrices: A new tool for vector-sensor signal processing. Signal Process 84 (2004), 11771199.
11. Mallat S. G., Zhang Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. on Signal Processing 41, 33973415 (1993).
12. D. P. Mandic, C. Jahanchahi and C. C. Took, A quaternion gradient operator and its applications. IEEE Signal Processing Letters 18 (2011), 4750.
13. Moxey C. E., Sangwine S. J., Ell T. A.: Hypercomplex correlation techniques for vector images. IEEE Trans. on Signal Processing, 51, 19411953 (2003).
14. Y. C. Pati, R. Rezaiifar and P. S. Krishnaprasad, Orthogonal Matching Pursuit: recursive function approximation with applications to wavelet decomposition. In Conf. Record of the Asilomar Conf. on Signals, Systems and Comput., 1993, pages 4044.
15. E. Smith and M. S. Lewicki, Efficient coding of time-relative structure using spikes. Neural Comput. 17 (2005), 1945.
16. C. C. Took and D. P. Mandic, Quaternion-valued stochastic gradient-based adaptive IIR filtering. IEEE Trans. on Signal Processing, 58 (2010), 38953901.
17. Tropp J. A., Wright S. J.: Computational methods for sparse solution of linear inverse problems. Proceedings of the IEEE, 98, 948958 (2010).
18. J. Via, D. P. Palomar, L. Vielva and I. Santamaria, Quaternion ICA from second-order statistics. IEEE Trans. on Signal Processing, 59 (2011), 15861600.