Self-supervised training of deep denoisers in multi-coil MRI considering noise correlations

Deep learning-based denoising methods have shown powerful results for improving the signal-to-noise ratio of magnetic resonance (MR) images, mostly by leveraging supervised learning with clean ground truth. However, acquiring clean ground truth images is often expensive and time-consuming. Self supervised methods have been widely investigated to mitigate the dependency on clean images, but mostly rely on the suboptimal splitting of K-space measurements of an image to yield input and target images for ensuring statistical independence. In this study, we investigate an alternative self-supervised training method for deep denoisers in multi-coil MRI, dubbed Coil2Coil (C2C), that naturally split and combine the multi-coil data among phased array coils, generating two noise-corrupted images for training. This novel approach allows exploiting multi-coil redundancy, but the images are statistically correlated and may not have the same clean image. To mitigate these issues, we propose the methods to pproximately decorrelate the statistical dependence of these images and match the underlying clean images, thus enabling them to be used as the training pairs. For synthetic denoising experiments, C2C yielded the best performance against prior self-supervised methods, reporting outcome comparable even to supervised methods. For real-world denoising cases, C2C yielded consistent performance as synthetic cases, removing only noise structures.