Computing the hilbert Transform

I want to apply the hilbert transform for the gray scale image. The hilbert function in signal processing toolbox is applied to the time series signal in one dimension. But i want it for 2D image

[Walter Roberson]

Note: hilbert() will accept 2D arrays on input, but it will only apply the transform to the columns.

[Walter Roberson]

2D fft relies upon fft being composeable along the 2 directions. I see that hilbert is order 4, so I am concerned that if you were to try hilbert(hilbert(M).').' as you might with fft, that the double phase-change would give undesirable effects. The math is not at all obvious to me.

I wonder if -hilbert(hilbert(M).').' might happen to be correct? But that is speculation.