There is an unblurred image $g$ and a blurred image $x$.
Their relationship is expressed by the following formula using $psf$(point spread fucntion, size is $5×5$ kernel).
$g = x \otimes psf\tag 1$
where $\otimes$ is 2D convoluition. If I write the above formula by matrix operation, also, I am thinking about blind deconvolution
$\nabla^2\mathbf{g} = \nabla^2\mathbf{x\;PSF^{(k)}}\tag 2$
where, $\mathbf{g}$ and $\mathbf{x}$ is $N×N$ matrices, and $\mathbf{PSF}$ is $N^2×N^2$ Toeplitz matrices,$\nabla^2$ is the second order differential operator.
I want to solve an optimization problem that incorporates Equation $(2)$.
In the process of optimizing $\mathbf{x}$, I also want to optimize $\mathbf{PSF}$ by the conjugate gradient method.
$$\mathbf{PSF}^{(k+1)} \leftarrow \text{Conjugate Gradient Method}(\mathbf{\nabla^2g}, \;\mathbf{\nabla^2x}^{(k+1)},\; \mathbf{PSF}^{(k)})$$
[What I want to do]
In the process of optimizing $\mathbf{x}$, I also want to optimize $\mathbf{PSF^{(k)}}$ by the conjugate gradient method.
[What I want you to tell me]
From the following questions, [How to estimate filters using conjugate gradient?]
should I think of deconvolution in frequency space?
Or should I update psf by matrix operation in a different way?
