Color Extension of Monogenic Wavelets with Geometric Algebra : Application to Color Image Denoising

Raphaël Soulard (1) , Philippe Carré (1)

1 SIC

We define a color monogenic wavelet transform. This is based on the recent grayscale monogenic wavelet transform and an extension to color signals aimed at defining non-marginal tools. Wavelet based color image processing schemes have mostly been made by using a grayscale tool separately on color channels. This may have some unexpected effect on colors because those marginal schemes are not necessarily justified. Here we propose a definition that considers a color (vector) image right at the beginning of the mathematical definition so we can expect to bring an actual color wavelet transform - which has not been done so far to our knowledge. This so provides a promising multiresolution color geometric analysis of images. We show an application of this transform with a statistical modeling of coefficients for color denoising issue.

Mots clés: Color Wavelets; Analytic; Monogenic; Wavelet transforms; Image analysis; Denoising

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Raphaël Soulard, Philippe Carré. Color Extension of Monogenic Wavelets with Geometric Algebra : Application to Color Image Denoising. 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics (ICCA9), Jul 2011, Weimar, Germany. pp.179. ⟨hal-00618153⟩