In our setting, multichannel data are modeled as the concatenation of M so-called observations or monochannel data. For instance, in the case of color images, theses observations are the three color layers Red, Blue, Green. In a more general framework, multichannel data can be the concatenation of physical observations made at different frequency channels. This is the case of multispectral or hyperspectral imaging. Formally, assuming that each observation has t samples, such multichannel are written as  m x t matrix.

Diversity can then be found in each observation separately and also across the observations. In the case of hyperspectral imaging, each observation has an intrinsic structure; a fixed pixel is also a spectrum that has also a given structure. For instance, real world hyperspectral images have hyperspectral pixels that are absorption spectra.

Below, the image features a Mars Express observation. A fixed pixel is then a unidimensional spectrum.

Then extending the morphological diversity to the multichannel case requires accounting for both spatial and spectral morphologies.

Applications :

Multichannel Morphological Component Analysis for color images