  A large number of coils are able to provide enhanced signal-to-noise ratio
and improve imaging performance in parallel imaging. Nevertheless, the
increasing growth of coil number simultaneously aggravates the drawbacks of
data storage and reconstruction speed, especially in some iterative
reconstructions. Coil compression addresses these issues by generating fewer
virtual coils. In this work, a novel variable augmentation network for
invertible coil compression termed VAN-ICC is presented. It utilizes inherent
reversibility of normalizing flow-based models for high-precision compression
and invertible recovery. By employing the variable augmentation technology to
image/k-space variables from multi-coils, VAN-ICC trains invertible networks by
finding an invertible and bijective function, which can map the original data
to the compressed counterpart and vice versa. Experiments conducted on both
fully-sampled and under-sampled data verified the effectiveness and flexibility
of VAN-ICC. Quantitative and qualitative comparisons with traditional non-deep
learning-based approaches demonstrated that VAN-ICC can carry much higher
compression effects. Additionally, its performance is not susceptible to
different number of virtual coils.
