# 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="/files/4jG103qvjMCpeAell1Z4" alt=""><figcaption><p>Noise verification</p></figcaption></figure>


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