Wavelet <em>q-</em>Fisher Information for Scaling Signal Analysis

Abstract

Abstract: This article first introduces the concept of wavelet <em>q</em>-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<em> q</em>. In the limit of <em>q → 1,</em> wavelet <em>q</em>-Fisher information reduces to the standard wavelet Fisher information and for <em>q > 2</em> 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<em> q</em>-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.<em>263 </em>encoded video signals is presented.

Keywords

• scaling processes
• &lt;em&gt; 1/ƒ &lt;sup&gt;α&lt;/sup&gt;&lt;/em&gt; processes
• wavelet   information  measures
• &lt;em&gt;q&lt;/em&gt;-Fisher  information
• fractional Gaussian  noise
• structural change  detection/location
• breakpoint detection&lt;br /&gt;