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

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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.

Accepted Answer

Matt J
Matt J on 20 Oct 2021
Edited: Matt J on 21 Oct 2021
Matt J
Matt J on 22 Oct 2021
Edited: Matt J on 22 Oct 2021
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.

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