  Image enhancement approaches often assume that the noise is signal
independent, and approximate the degradation model as zero-mean additive
Gaussian. However, this assumption does not hold for biomedical imaging systems
where sensor-based sources of noise are proportional to signal strengths, and
the noise is better represented as a Poisson process. In this work, we explore
a sparsity and dictionary learning-based approach and present a novel
self-supervised learning method for single-image denoising where the noise is
approximated as a Poisson process, requiring no clean ground-truth data.
Specifically, we approximate traditional iterative optimization algorithms for
image denoising with a recurrent neural network that enforces sparsity with
respect to the weights of the network. Since the sparse representations are
based on the underlying image, it is able to suppress the spurious components
(noise) in the image patches, thereby introducing implicit regularization for
denoising tasks through the network structure. Experiments on two bio-imaging
datasets demonstrate that our method outperforms the state-of-the-art
approaches in terms of PSNR and SSIM. Our qualitative results demonstrate that,
in addition to higher performance on standard quantitative metrics, we are able
to recover much more subtle details than other compared approaches. Our code is
made publicly available at https://github.com/tacalvin/Poisson2Sparse
