Suppression of Independent and Correlated Noise with Similarity-based Unsupervised Deep Learning

Denoising is one of the most important data processing tasks and is generally a prerequisite for downstream image analysis in many fields. Despite their superior denoising performance, supervised deep denoising methods require paired noise-clean or noise-noise samples often unavailable in practice. On the other hand, unsupervised deep denoising methods such as Noise2Void and its variants predict masked pixels from their neighboring pixels in single noisy images. However, these unsupervised algorithms only work under the independent noise assumption while real noise distributions are usually correlated with complex structural patterns. Here we propose the first-of-its-kind feature similarity-based unsupervised denoising approach that works in a nonlocal and nonlinear fashion to suppress not only independent but also correlated noise. Our approach is referred to as Noise2Sim since different noisy sub-images with similar signals are extracted to form as many as possible training pairs so that the parameters of a deep denoising network can be optimized in a self-learning fashion. Theoretically, the theorem is established that Noise2Sim is equivalent to the supervised learning methods under mild conditions. Experimentally, Noise2Sim achieves excellent results on natural, microscopic, low-dose CT and photon-counting micro-CT images, removing image noise independent or not and being superior to the competitive denoising methods. Potentially, Noise2Sim would open a new direction of research and lead to the development of adaptive denoising tools in diverse applications.