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Both of them seem to do the same task. Wherever the pixel values within the image refers to something that was not there in the original image, we call that pixel to be affected by noise. If this noise is less, we apply noise reduction. When the pixel refers to totally random value, we apply image inpainting.

So is image inpainting just an extreme case of image denoising?

Also if a large portion of pixels get affected, we call that a "noise" and need to apply denoising algorithms; whereas when a small portion gets affected like a scratch on the image, we apply inpainting techniques. But my question is: that scratch can also be regarded as a noise only. So why dont we call that process image denoising?

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  • $\begingroup$ Do you mean "inpainting"? $\endgroup$ – Adi Shavit Dec 12 '16 at 7:21
  • $\begingroup$ Yes, sorry. Corrected. $\endgroup$ – user257330 Dec 12 '16 at 11:45
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Inpainting solves a binary problem of missing data. These masked or missing pixels to not contain information that is used in the reconstruction. Also, is it assumed that non missing pixels are to remain as is.

Denoising usually refers to the situation where all the pixels contain some noise component, which often also has some global prior independent of the image content. The algorithm tries to remove the noise from all the pixels, and uses the information inside these noisy pixels for the reconstruction and estimation.

The problems are not unrelated and could be reduced to private extreme cases of each other but in general they solve different types of problems.

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In my opinion, both can be referred as the restoration problem: $$ Y = R(I) + N $$ where $Y\in \mathbb{R}^{m\times n}$ is the observation, $I\in \mathbb{R}^{m_0\times n_0}$ is the original image, $R: \mathbb{R}^{m_0\times n_0} \mapsto \mathbb{R}^{m\times n}$ is a linear degradation operator that could represent convolution (image blurring, low resolution image, etc.), masking, mixturing etc.., $N$ is the observation noise.

By denoising, it means that $R=I$ an identity projection and $m_0=m, n_0=n$.

By inpainting, it means that $R$ is some masking and selection operator.

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