Hey!

I is the flattened image (i.e., a matrix where each row represents the RGB values of a single pixel)

T and N are some matrices, basically of appropriate dimensions such that the transformation you quoted results in an image of the same shape as the original and also such that we can optimize certain objectives with respect to the variables that define the transformation.

The why this is the desired transformation is a tricky question, it's definitely not the only and quite probably not the best way to formulate this problem - just the first way that I tried and worked reasonably well. I tried to explain my intuition for this in the article after the definition.