Let $X$ and $K$ be an image and a Point Spread Function (PSF), respectively.
The blurred image $B$ is obtained as follows
$$B = X * K$$
I want to solve the following general regularization problem
$$\min_X \left\|X * K - B\right\|_2^2 + \lambda \| f(X) \|_2^2$$
where $f$ is a regularization function. In some literature (e.g. Blur kernel estimation via salient edges and low rank prior for blind image deblurring) I have seen, the authors use the FFT to solve such a problem. However, I cannot find any resources that show the procedure. My questions are:
- How one can use FFT to solve the above problem?
- Is there any condition that must be satisfied to use FFT?