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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:

  1. I up-sampled the image by factor of 2,
  2. and then added some random noise multiplied by different weights,
  3. and then down-sampled again using bi-cubic in both samplings.
  4. 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?

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