Relevance of Wavelet Shape Selection in a complex signal

In wavelet analysis, the signal reconstruction and statistical estimators are strongly influenced by the wavelet shape that controls the time-frequency localization properties. However, this dependency does not imply that the wavelet form is physically relevant to extract spatially invariant wavelet-based shape signatures. A new statistical estimator is proposed in order to quantify the influence of the wavelet on the spatial detection. This indicator is then used to analyze signals obtained from the topography of abraded surfaces. It is shown that the Coiflet wavelet is physically adapted to reproduce the elementary mechanical process which creates the abrasion of the surface. Using 8 different wavelets, the analysis of the signal obtained by scanning the abraded surface leads to the same spatial localization regardless the parameters of the abrasive process and whatever the wavelet shapes. No statistical difference related to the type of wavelets is found between the indicators (RMS, spectral moments...) extracted from the reconstructed signals calculated on different scales and for various abrasive processes. If the wavelet decomposition is seen as a multiscale microscope, a surface can be seen in different ways according to the type of wavelets. However, the morphological changes of the surface caused by external mechanical causes and characterized by several statistical parameters are statistically similar regardless the shape of the wavelets. (C) 2013 Elsevier Ltd. All rights reserved.