A use case of autoencoders (in particular, of the decoder or generative model of the autoencoder) is to denoise the input. This type of autoencoders, called denoising autoencoders, take a partially corrupted input and they attempt to reconstruct the corresponding uncorrupted input. There are several applications of this model. For example, if you had a corrupted image, you could potentially recover the uncorrupted one using a denoising autoencoder.

Autoencoders and PCA are related:

an autoencoder with a single fully-connected hidden layer, a linear activation function and a squared error cost function trains weights that span the same subspace as the one spanned by the principal component loading vectors, but that they are not identical to the loading vectors.

For more info, have a look at the paper From Principal Subspaces to Principal Components with Linear Autoencoders (2018), by Elad Plaut.

A use case of autoencoders (in particular, of the decoder or generative model of the autoencoder) is to denoise the input. This type of autoencoders, called denoising autoencoders, take a partially corrupted input and they attempt to reconstruct the corresponding uncorrupted input. There are several applications of this model. For example, if you had a corrupted image, you could potentially recover the uncorrupted one using a denoising autoencoder.

Autoencoders and PCA are related:

an autoencoder with a single fully-connected hidden layer, a linear activation function and a squared error cost function trains weights that span the same subspace as the one spanned by the principal component loading vectors, but that they are not identical to the loading vectors.

For more info, have a look at the paper From Principal Subspaces to Principal Components with Linear Autoencoders (2018), by Elad Plaut. See also this answer, which also explains the relation between PCA and autoencoders.