Recovering a high-quality image from noisy indirect measurements is an important problem with many applications. For such inverse problems, supervised deep convolutional neural network (CNN)-based denoising methods have shown strong results, but the success of these supervised methods critically depends on the availability of a high-quality training dataset of similar measurements. For image denoising, methods are available that enable training without a separate training dataset by assuming that the noise in two different pixels is uncorrelated. However, this assumption does not hold for inverse problems, resulting in artifacts in the denoised images produced by existing methods. Here, we propose Noise2Inverse, a deep CNN-based denoising method for linear image reconstruction algorithms that does not require any additional clean or noisy data. Training a CNN-based denoiser is enabled by exploiting the noise model to compute multiple statistically independent reconstructions. We develop a theoretical framework which shows that such training indeed obtains a denoising CNN, assuming the measured noise is element-wise independent, and zero-mean. On simulated CT datasets, Noise2Inverse demonstrates an improvement in peak signal-To-noise ratio and structural similarity index compared to state-of-The-Art image denoising methods, and conventional reconstruction methods, such as Total-Variation Minimization. We also demonstrate that the method is able to significantly reduce noise in challenging real-world experimental datasets.

Deep learning, image reconstruction, inverse problems, reconstruction algorithms, tomography
IEEE Transactions on Computational Imaging
Real-Time 3D Tomography
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Hendriksen, A.A, Pelt, D.M, & Batenburg, K.J. (2020). Noise2Inverse: Self-Supervised Deep Convolutional Denoising for Tomography. IEEE Transactions on Computational Imaging, 6, 1320–1335. doi:10.1109/TCI.2020.3019647