  Image denoising is a prerequisite for downstream tasks in many fields.
Low-dose and photon-counting computed tomography (CT) denoising can optimize
diagnostic performance at minimized radiation dose. Supervised deep denoising
methods are popular but require paired clean or noisy samples that are often
unavailable in practice. Limited by the independent noise assumption, current
unsupervised denoising methods cannot process correlated noises as in CT
images. Here we propose the first-of-its-kind similarity-based unsupervised
deep denoising approach, referred to as Noise2Sim, that works in a nonlocal and
nonlinear fashion to suppress not only independent but also correlated noises.
Theoretically, Noise2Sim is asymptotically equivalent to supervised learning
methods under mild conditions. Experimentally, Nosie2Sim recovers intrinsic
features from noisy low-dose CT and photon-counting CT images as effectively as
or even better than supervised learning methods on practical datasets visually,
quantitatively and statistically. Noise2Sim is a general unsupervised denoising
approach and has great potential in diverse applications.
