Figure 1.

An overview of the proposed self-supervised collaborative training framework. A raw undersampled k-space data sequence ${\mathbf{y}}_{\Omega }^t$ is undersampled from the fully sampled data using an undersampled mask $P^t$ retrospectively, and then two k-space data sequences ${\mathbf{y}}_{\Theta }^t$ and ${\mathbf{y}}_{\Lambda }^t$ are augmented from ${\mathbf{y}}_{\Omega }^t$. In the considered scenario, ${\mathbf{y}}_{\Theta }^t$ and ${\mathbf{y}}_{\Lambda }^t$ are reundersampled from ${\mathbf{y}}_{\Omega }^t$ using reundersampled mask ${\mathbf{P}}_{\Theta }^t$ and ${\mathbf{P}}_{\Lambda }^t$, respectively. Next, the two networks received inputs from zero-filling image sequences of ${\mathbf{y}}_{\Theta }^t$ and ${\mathbf{y}}_{\Lambda }^t$. The predicted image sequences of networks are transformed to the k-space data $f_{\Theta }\left(y_{\Theta }^t\right)$ and $f_{\Lambda }\left(y_{\Lambda }^t\right)$ by two-dimensional Fourier transform. Afterward, a co-training loss is calculated using ${\mathbf{y}}_{\Omega }^t$, $f_{\Theta }\left(y_{\Theta }^t\right)$ and $f_{\Lambda }\left(y_{\Lambda }^t\right)$. The backbone reconstruction network can flexibly adopt different iterative un-rolled network, such as CRNN, k-t NEXT and SLR-Net. Collaborative network-1 and collaborative network-2 have the same network structure but different weight parameters ${\theta }_{\Theta }$ and ${\theta }_{\Lambda }$ respectively.