Recovering a high-quality image from noisy indirect measurement 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 their success 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 output of existing methods. Here, we propose Noise2Inverse, a deep CNN-based denoising method for linear inverse problems in imaging 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 a substantial improvement in peak signal-to-noise ratio (> 2dB) and structural similarity index (> 30%) compared to 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.

利用深度卷积神经网络（CNN）开发了一种图像去噪方法：Noise2Inverse，可以应用于线性图像重建算法，无需任何额外的干净或噪声数据，通过利用噪声模型计算多个统计独立的重建来实现训练，该方法在模拟CT数据集和现实实验数据集中均显示出优于现有状态下的图像去噪方法和传统重建方法，能够显著降低噪声。

Noise2Inverse：用于断层 tomography 的自监督深度卷积去噪