Ambilight without computer - µC
Welcome to EE.SE.

I'll first say that apart from a few small misspellings your English looks perfectly understandable to me. Though I may be in the advantage of growing up multi-lingual.

First I wonder whether you need to process all of the pixels?

If you need to make one LED strip on the side light up, get yourself a few JPEG images from the internet, or some show stills from IMDB.com, just some random ones, and see if you can work out with those how few lines/columns of pixels you really need to get a good average.

I'm willing to bet you can easily work with only 1/8th the pixels for just one single channel side-LED.

And even if you need to do 4 edges with 12 different lamps on each edge, you can ignore the middle 75% of the image and probably still only use a simplified set of pixels. That's probably what the Scimo does as well.

That said, I would suggest you look at ARM development boards.

I'm assuming that you are supposed to also work without an operating system on the board, so then I'd suggest looking at Olimex or Brand-Own boards. Companies like Texas Instruments and Atmel make pretty affordable demo-boards using their Cortex-M series controllers and very well designed.

With a Cortex-M series that you choose well (I'd expect M3 or M4) you could get a 80MHz core clock and loads of internal hardware support for quick interfaces that would probably allow you to get all of the data out of such a video chip on time. They will likely not have the RAM you wanted, but if you decide on pixels to keep and to throw away while you read the data and you do it smartly, I'm sure you can do with 1/10th the RAM you thought you needed.