Denoising Autoencoders

Denoising autoencoders are autoencoders that remove noise from an image.

We feed a noisy version of the image, where noise has been added via digital alterations. The noisy image is fed to the encoder-decoder architecture, and the output is compared with the ground truth image.

The denoising autoencoder gets rid of noise by learning a representation of the input where the noise can be filtered out easily.

While removing noise directly from the image seems difficult, the autoencoder performs this by mapping the input data into a lower-dimensional manifold (like in undercomplete autoencoders), where filtering of noise becomes much easier.

Model

Source: https://www.v7labs.com/blog/autoencoders-guide

With this approach, our model isn't able to simply develop a mapping which memorizes the training data because our input and target output are no longer the same.
Rather, the model learns a vector field for mapping the input data towards a lower-dimensional manifold (recall from my earlier graphic that a manifold describes the high density region where the input data concentrates); if this manifold accurately describes the natural data, we've effectively "canceled out" the added noise.

Source: https://www.jeremyjordan.me/autoencoders/

The above figure visualizes the vector field described by comparing the reconstruction of x with the original value of x. The yellow points represent training examples prior to the addition of noise. As you can see, the model has learned to adjust the corrupted input towards the learned manifold.
It's worth noting that this vector field is typically only well behaved in the regions where the model has observed during training.
In areas far away from the natural data distribution, the reconstruction error is both large and does not always point in the direction of the true distribution.

References

https://www.v7labs.com/blog/autoencoders-guide

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Denoising Autoencoders

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