Images have smotth edges or abrupt edges. Fourier transforms are efficient but does not show efficiency sometimes.
Because, Fourier transforms are kind of sum of sine waves which are not localized is time and wave which means
the oscillates infinitely in time and space. This is why, space and time well localized something was need indeed.
This brings the "WAVELET". Wavelets are rapidly changing or plunging wave like oscillations which have a mean of zero.
The above figure is an wavelet. Unlike sine waves it hase locality in time and space. which means this oschillates finitely in time and spcace.
Now, gabour..Gabor wavelets are wavelets invented by Dennis Gabor using complex functions constructed to serve as a basis for Fourier transforms in information theory applications.
Or you can view https://en.wikipedia.org/wiki/Gabor_wavelet
