Self-supervised denoising of Nyquist-sampled volumetric images via deep learning.

Purpose: Deep learning has demonstrated excellent performance enhancing noisy or degraded biomedical images. However, many of these models require access to a noise-free version of the images to provide supervision during training, which limits their utility. Here, we develop an algorithm (noise2Nyquist) that leverages the fact that Nyquist sampling provides guarantees about the maximum difference between adjacent slices in a volumetric image, which allows denoising to be performed without access to clean images. We aim to show that our method is more broadly applicable and more effective than other self-supervised denoising algorithms on real biomedical images, and provides comparable performance to algorithms that need clean images during training. Approach: We first provide a theoretical analysis of noise2Nyquist and an upper bound for denoising error based on sampling rate. We go on to demonstrate its effectiveness in denoising in a simulated example as well as real fluorescence confocal microscopy, computed tomography, and optical coherence tomography images. Results: We find that our method has better denoising performance than existing self-supervised methods and is applicable to datasets where clean versions are not available. Our method resulted in peak signal to noise ratio (PSNR) within 1 dB and structural similarity (SSIM) index within 0.02 of supervised methods. On medical images, it outperforms existing self-supervised methods by an average of 3 dB in PSNR and 0.1 in SSIM. Conclusion: noise2Nyquist can be used to denoise any volumetric dataset sampled at at least the Nyquist rate making it useful for a wide variety of existing datasets.