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

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. 1 ha l-0 06 18 15 3, v er si on 1 31 A ug 2 01 1 Author manuscript, published in "9th International Conference on Clifford Algebras and their Applications in Mathematical Physics (ICCA9), Weimar : Germany (2011)"