  Accurate analysis of microscopy images is hindered by the presence of noise.
This noise is usually signal-dependent and often additionally correlated along
rows or columns of pixels. Current self- and unsupervised denoisers can address
signal-dependent noise, but none can reliably remove noise that is also row- or
column-correlated. Here, we present the first fully unsupervised deep
learning-based denoiser capable of handling imaging noise that is
row-correlated as well as signal-dependent. Our approach uses a Variational
Autoencoder (VAE) with a specially designed autoregressive decoder. This
decoder is capable of modeling row-correlated and signal-dependent noise but is
incapable of independently modeling underlying clean signal. The VAE therefore
produces latent variables containing only clean signal information, and these
are mapped back into image space using a proposed second decoder network. Our
method does not require a pre-trained noise model and can be trained from
scratch using unpaired noisy data. We show that our approach achieves
competitive results when applied to a range of different sensor types and
imaging modalities.
