Matlab Hilbert Transform in C++
If your application can use LGPL open-source code, you could reuse the code for the Remez exchange algorithm in the GNU Octave source.  I've got a standalone library that does that at www.ke5fx.com/dsplib.zip .  See if the function DSP_FIR_PM_Hilbert_transformer_design() does what you want.

The FIR filters implemented by my library are one-dimensional affairs, so if you actually need to do a 2D transform, that would be left as an exercise, so to speak.  Contributions back to dsplib are welcome!