I'm trying to prove the fact that the super-resolution problem is an ill-posed problem.
Having a single low-resolution image, we can generate multiple high-resolution images.
Which also known by applying bi-cubic interpolation is similar to up-sampling into the average image of the all multiple versions.
In order to achieve this:
- I up-sampled the image by factor of 2,
- and then added some random noise multiplied by different weights,
- and then down-sampled again using bi-cubic in both samplings.
- Also by applying Gaussian with different kernels to the noisy image before down-sampling.
Result: I can't achieve close to zero error when I measure the different between the original lr and the down-sampled lr.
Q: How it is possible to down-sample different versions of super-resolved images and achieve zero error to prove the fact of ill-posed problem?