> For the complete documentation index, see [llms.txt](https://docs.inferix.io/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.inferix.io/inferix-whitepaper/high-level-description/noise-verification.md).

# Noise verification

Different from proof of ownership schemes [\[2\]](/inferix-whitepaper/references.md#2), [\[3\]](/inferix-whitepaper/references.md#3), the verification of watermark requires a key. Given an image $$J$$ and a verification key $$K\_{\mathtt{verif}}$$, we first try to recover a watermark $$\hat{W}$$ from $$J$$ using a decoding function $$\mathcal{D}$$:

$$
\hat{W} = \mathcal{D} \thinspace (J, K\_{\mathtt{verif}})
$$

Next $$\hat{W}$$ is compared against $$W$$, if the deviation is above some threshold $$T$$:

$$
\lVert \hat{W} - W \rVert \geq T
$$

then $$J$$ will be accepted otherwise rejected.

<figure><img src="https://3032367557-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FcE7ARktdPinaZgrdSJOX%2Fuploads%2FtGNydTK0sMThcWSfnJPs%2Fnoise-verification.svg?alt=media&amp;token=e0fbac3f-ef3f-43ff-a7e7-87247460f3b4" alt=""><figcaption><p>Noise verification</p></figcaption></figure>