From what I understand its the analytic signal equivalent but for a 2D signal (like an image). If so, I am having trouble visualization what the envelope of a image and instantaneous amplitude/phase means.

Can anyone kindly explain this? What information does it have that a regular Fourier transform cannot convey?

From what I understand the monogenic signal is the analytic signal equivalent but for a 2D signals like an image. 

If so, I am having trouble visualization what the envelope of a image and instantaneous amplitude/phase means.

Can anyone kindly explain this? 

What information does it have that a regular Fourier transform cannot convey?