How do I obtain FFT of nabla operator F(▽）?

I would like to write a matlab program that solves a least squares problem by using FFT(Fast Fourier Transform), but I don't know how to computes this in matlab:F(▽^T▽),where F means FFT,and ▽ is applied on an M×N image.

Waiting for your kindly help,

Thank you in advance.

[KSSV]

Have a look on gradient.

Answer 1

[Matt J]

4*fft2(del2(Image))

[Suki Liu]

Thanks for your help! It‘s’ my fault for not explaining my question in detail.In fact，F(▽^T▽) is the denominator,and the entire equation is F(▽^T▽G)=F(L),which equals F(G)=F(L)/F(▽^T▽)，G，L are both M×N image.To obtain the value of G，I need to compute F(▽^T▽) .Thanks again!

[Matt J]

You can use pcg() to solve the equation. It will let you specify the operator in the functional form that I have proposed.

Your equation is ill-posed, however, because ▽^T▽ is singular. You probably need to add some regularization term.