I was reading a paper 'A Flexible Framework for Local Phase Coherence Computation' (paper URL) on using wavelets for local phase coherence. I just want to be sure. Is the gabor wavelet the same as the gabor function in the gabor transform (STFT)? If not, can we use a Windowed Fourier Transform instead?
The Gabor wavelet is (almost) the same as the Morlet wavelet (some authors distinguish these two by an additional constant to fulfill the wavelet's admissibility condition). And yes, it is the same function as in the Gabor transform (gaussian windowed oscillation).
The application of phase coherence should be independent of the underlying wavelet and the nature of the transform (Wavelet, Gabor/STFT, other weird metrics). Essentially important is the concept of reproducing kernels and the intrinsic (Heisenberg) uncertainty that influence you measure of phase coherence and must be taken care of.