Closed wangherr closed 5 months ago
Hi wangherr,
$x_0$ denotes the unknown groundtruth image and $Ax_0$ denotes the known measurements $y$. In case of noisy inverse problems, $y=Ax_0^* + noise$.
for line 8,
I can understand it in inpainting.
if in others task, such as Gaussian deblur,
1, will the A A^T x*_0
to be x_0
(groundtruth image)?
2, will the I - A A^T
to be 0
?
thanks!
As you have rightly pointed out, line 8 is self-explanatory for inpainting tasks. For Gaussian deblur, it is not clear what $A^T$ would be in this case. However, note that all linear inverse problems can be expressed as inpainting tasks at the cost of a big tedious measurement matrix $A$. Therefore, our algorithm generalizes to other linear inverse tasks.
In practice, we borrow the measurement operators from DPS, which seems to work reasonably well.
Note:- Q1 and Q2 above are incorrect because there is dimension mismatch between $A^T$ and $x_0$. Above answer is for $A^TAx_0$.
Is 'line 8' only used in inpainting tasks in practice?
No, it is used for all the inverse tasks where A^T and A are chosen as per the DPS codebase. For inpainting, line 8 is exact and for other inverse tasks, it is an approximation.
What is the meaning of
x*_0
orAx*_0
? I can't find any definition.Thanks!