  Deep Learning based methods have emerged as the indisputable leaders for
virtually all image restoration tasks. Especially in the domain of microscopy
images, various content-aware image restoration (CARE) approaches are now used
to improve the interpretability of acquired data. Naturally, there are
limitations to what can be restored in corrupted images, and like for all
inverse problems, many potential solutions exist, and one of them must be
chosen. Here, we propose DivNoising, a denoising approach based on fully
convolutional variational autoencoders (VAEs), overcoming the problem of having
to choose a single solution by predicting a whole distribution of denoised
images. First we introduce a principled way of formulating the unsupervised
denoising problem within the VAE framework by explicitly incorporating imaging
noise models into the decoder. Our approach is fully unsupervised, only
requiring noisy images and a suitable description of the imaging noise
distribution. We show that such a noise model can either be measured,
bootstrapped from noisy data, or co-learned during training. If desired,
consensus predictions can be inferred from a set of DivNoising predictions,
leading to competitive results with other unsupervised methods and, on
occasion, even with the supervised state-of-the-art. DivNoising samples from
the posterior enable a plethora of useful applications. We are (i) showing
denoising results for 13 datasets, (ii) discussing how optical character
recognition (OCR) applications can benefit from diverse predictions, and are
(iii) demonstrating how instance cell segmentation improves when using diverse
DivNoising predictions.
