it needs to be as fast as possible
Then you're asking the wrong question.
Code it in assembler, with different versions for each significant architecture variant you support.
Use as a guide the output from a good C++ compiler with optimisation, because it probably knows some tricks that you don't. But you'll probably be able to think of some improvements, because C++ doesn't necessarily convey to the compiler all information that might be useful for optimisation. For example, C++ doesn't have the C99 keyword restrict. Although in that particular case many C++ compilers (including MSVC) do now support it, so use it where possible.
Of course if you mean, "I want it to be fast, but not to the extent of going outside C# or C++", then the answer's different ;-)
I would expect C# to at least approach the performance of similar-looking C++ in a lot of cases. I assume of course that the program will be running long enough that the time the JIT itself takes is irrelevant, but if you're processing much video then that seems likely. But I'd also expect there to be certain things which if you do them in unsafe C#, will be far slower than the equivalent thing in C++. I don't know what they are, because all my experience of JITs is in Java rather than CLR. There might also be things which are slower in C++, for instance if your algorithm makes any calls back into C# code.
Unfortunately the only way to be sure how close it is is to write both and test them, which kind of misses the point that writing the C++ version is a bunch of extra effort. However, you might be able to get a rough idea by hacking some quick code which approximates the processing you want to do, without necessarily doing all of it or getting it right. If you algorithm is going to loop over all the pixels and do a few FP ops per pixel, then hacking together a rough benchmark should take all of half an hour.
Usually I would advise against starting out thinking "this needs to be as fast as possible". Requirements should be achievable, and by definition "as X as possible" is only borderline achievable. Requirements should also be testable, and "as X as possible" isn't testable unless you somehow know a theoretical maximum. A more friendly requirement is "this needs to process video frames of such-and-such resolution in real time on such-and-such a speed CPU", or "this needs to be faster than our main competitor's product". If the C# version does that, with a bit to spare to account for unexpected minor issues in the user's setup, then job done.