Benjamin Salmon

Alexander Krull, Hector Basevi, Benjamin Salmon et al.

We present a fresh perspective on shot noise corrupted images and noise removal. By viewing image formation as the sequential accumulation of photons on a detector grid, we show that a network trained to predict where the next photon could arrive is in fact solving the minimum mean square error (MMSE) denoising task. This new perspective allows us to make three contributions: We present a new strategy for self-supervised denoising, We present a new method for sampling from the posterior of possible solutions by iteratively sampling and adding small numbers of photons to the image. We derive a full generative model by starting this process from an empty canvas. We call this approach generative accumulation of photons (GAP). We evaluate our method quantitatively and qualitatively on 4 new fluorescence microscopy datasets, which will be made available to the community. We find that it outperforms supervised, self-supervised and unsupervised baselines or performs on-par.

Benjamin Salmon, Alexander Krull

Traditional supervised denoisers are trained using pairs of noisy input and clean target images. They learn to predict a central tendency of the posterior distribution over possible clean images. When, e.g., trained with the popular quadratic loss function, the network's output will correspond to the minimum mean square error (MMSE) estimate. Unsupervised denoisers based on Variational AutoEncoders (VAEs) have succeeded in achieving state-of-the-art results while requiring only unpaired noisy data as training input. In contrast to the traditional supervised approach, unsupervised denoisers do not directly produce a single prediction, such as the MMSE estimate, but allow us to draw samples from the posterior distribution of clean solutions corresponding to the noisy input. To approximate the MMSE estimate during inference, unsupervised methods have to create and draw a large number of samples - a computationally expensive process - rendering the approach inapplicable in many situations. Here, we present an alternative approach that trains a deterministic network alongside the VAE to directly predict a central tendency. Our method achieves results that surpass the results achieved by the unsupervised method at a fraction of the computational cost.

Benjamin Salmon, Alexander Krull

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 benchmark our approach on microscopy datatsets from a range of imaging modalities and sensor types, each with row- or column-correlated, signal-dependent noise, and show that it outperforms existing self- and unsupervised denoisers.