There can be "fast" or "slow" transformation matrix: matrix transformation is matrix transformation, that all have the same speed (quite good).
I'm quite sure you cannot achieve the fix of such distortion (a very typical task) with just one matrix transformation, so the question is: can you find both easy-to-implement and fast solution for the distortion correction. That is your goal, right?
I don't think this is easy even if the parameters of distortion are already known. This article confirms my skepticism: http://sprg.massey.ac.nz/pdfs/2003_IVCNZ_408.pdf