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Wavelet q-Fisher Information for Scaling Signal Analysis
Department of Electrical Engineering, CINVESTAV-IPN Guadalajara Unit, 45019 Zapopán, Jalisco, Mexico
Department of Basic Sciences and Engineering (DCBeI), University of Caribe, 77528, Cancún, Q.Roo, Mexico
* Author to whom correspondence should be addressed.
Received: 10 May 2012; in revised form: 13 June 2012 / Accepted: 28 June 2012 / Published: 8 August 2012
Abstract: Abstract: This article first introduces the concept of wavelet q-Fisher information and then derives a closed-form expression of this quantifier for scaling signals of parameter α. It is shown that this information measure appropriately describes the complexities of scaling signals and provides further analysis flexibility with the parameter q. In the limit of q → 1, wavelet q-Fisher information reduces to the standard wavelet Fisher information and for q > 2 it reverses its behavior. Experimental results on synthesized fGn signals validates the level-shift detection capabilities of wavelet q-Fisher information. A comparative study also shows that wavelet q-Fisher information locates structural changes in correlated and anti-correlated fGn signals in a way comparable with standard breakpoint location techniques but at a fraction of the time. Finally, the application of this quantifier to H.263 encoded video signals is presented.
Keywords: scaling processes; 1/ƒ α processes; wavelet information measures; q-Fisher information; fractional Gaussian noise; structural change detection/location; breakpoint detection
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Ramírez-Pacheco, J.; Torres-Román, D.; Argaez-Xool, J.; Rizo-Dominguez, L.; Trejo-Sanchez, J.; Manzano-Pinzón, F. Wavelet q-Fisher Information for Scaling Signal Analysis. Entropy 2012, 14, 1478-1500.
Ramírez-Pacheco J, Torres-Román D, Argaez-Xool J, Rizo-Dominguez L, Trejo-Sanchez J, Manzano-Pinzón F. Wavelet q-Fisher Information for Scaling Signal Analysis. Entropy. 2012; 14(8):1478-1500.
Ramírez-Pacheco, Julio; Torres-Román, Deni; Argaez-Xool, Jesús; Rizo-Dominguez, Luis; Trejo-Sanchez, Joel; Manzano-Pinzón, Francisco. 2012. "Wavelet q-Fisher Information for Scaling Signal Analysis." Entropy 14, no. 8: 1478-1500.