Mollification Based on Wavelets

Mollification Based onWavelets

The mollification obtained by truncating the expansion in wavelets is studied, where the wavelets are so chosen that noise is reduced and the Gibbs phenomenon does not occur. The estimations of the error of approximation of the mollification are given for the case when the fractional derivative of a function is calculated. Noting that the estimations are applicable even when the orthogonality o...

Leather Inspection Based on Wavelets

This paper presents a new methodology to detect leather defects, based on the wavelet transform. The methodology uses a bank of optimised filters, where each filter is tuned to one defect type. Filter shape and wavelet sub-band are selected based the maximisation of the ratio between features values on defect regions and on normal regions. The proposed methodology can detect defects even when s...

Iris Recognition based on Wavelets

Wavelets based on orthogonal polynomials

In this paper we introduce and discuss a new method for the construction of time localized bases for polynomial subspaces of an L2-space with arbitrary weight. Our analysis is based upon the theory of orthogonal polynomials. Whereas the frequency localization will be predetermined by the choice of the polynomial spaces, the time localization will be realized by the choice of special basis funct...

Wavelets Based on Legendre Polynomials

We construct an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomial functions. The coefficients are taken as appropriate roots of Chebyshev polynomials of the second kind, as has been proposed in reference [1]. A multi-resolution analysis is implemented and illustrated with analytical data and real-life signals from turbulent flow fields.