Novel design of a fractional wavelet and its application to image denoising

Abstract

This paper proposes a new wavelet family based on fractional calculus. The Haar wavelet is extended to fractional order by a generalization of the associated conventional low-pass filter using the fractional delay operator Z−D. The high-pass fractional filter is then designed by a simple modulation of the low-pass filter. In contrast, the scaling and wavelet functions are constructed using the cascade Daubechies algorithm. The regularity and orthogonality of the obtained wavelet basis are ensured by a good choice of the fractional filter coefficients. An application example is presented to illustrate the effectiveness of the proposed method. Thanks to the flexibility of the fractional filters, the proposed approach provides better performance in term of image denoising.