Abstract
We define a colour monogenic wavelet transform. This is based on recent greyscale monogenic wavelet transforms and an extension to colour signals aimed at defining non-marginal tools. Wavelet based colour image processing schemes have mostly been made by separately using a greyscale tool on every colour channel. This may have some unexpected effects on colours because those marginal schemes are not necessarily justified. Here we propose a definition that considers a colour (vector) image right at the beginning of the mathematical definition so that we can expect to create an actual colour wavelet transform – which has not been done so far to our knowledge. This provides a promising multiresolution colour geometric analysis of images. We show an application of this transform through the definition of a full denoising scheme based on statistical modelling of coefficients.
Mathematics Subject Classification (2010). Primary 68U10; secondary 15A66, 42C40.
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Soulard, R., Carré, P. (2013). Colour Extension of Monogenic Wavelets with Geometric Algebra: Application to Color Image Denoising. In: Hitzer, E., Sangwine, S. (eds) Quaternion and Clifford Fourier Transforms and Wavelets. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0603-9_12
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DOI: https://doi.org/10.1007/978-3-0348-0603-9_12
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