Luminance-chrominance decompositions: a drawback

However, when considering natural images, the different color channels always share some common features which are inherited from the structures and from the objects depicted in the original image. It can be observed that along the objects' boundaries all color channels usually exhibit some simultaneous discontinuities or sharp transitions.
Roughly speaking, structures are correlated.

Thus, separate denoising of the three channels is often inadequate, and obviously far from optimal.

Vector / Multiband