Noise2Inverse: Self supervised deep convolutional denoising for linear inverse problems in imaging
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.
ArXiv