  Purpose: To develop a truly calibrationless reconstruction method that
derives ESPIRiT maps from uniformly-undersampled multi-channel MR data by deep
learning. Methods: ESPIRiT, one commonly used parallel imaging reconstruction
technique, forms the images from undersampled MR k-space data using ESPIRiT
maps that effectively represents coil sensitivity information. Accurate ESPIRiT
map estimation requires quality coil sensitivity calibration or autocalibration
data. We present a U-Net based deep learning model to estimate the
multi-channel ESPIRiT maps directly from uniformly-undersampled multi-channel
multi-slice MR data. The model is trained using fully-sampled multi-slice axial
brain datasets from the same MR receiving coil system. To utilize subject-coil
geometric parameters available for each dataset, the training imposes a hybrid
loss on ESPIRiT maps at the original locations as well as their corresponding
locations within the standard reference multi-slice axial stack. The
performance of the approach was evaluated using publicly available T1-weighed
brain and cardiac data. Results: The proposed model robustly predicted
multi-channel ESPIRiT maps from uniformly-undersampled k-space data. They were
highly comparable to the reference ESPIRiT maps directly computed from 24
consecutive central k-space lines. Further, they led to excellent ESPIRiT
reconstruction performance even at high acceleration, exhibiting a similar
level of errors and artifacts to that by using reference ESPIRiT maps.
Conclusion: A new deep learning approach is developed to estimate ESPIRiT maps
directly from uniformly-undersampled MR data. It presents a general strategy
for calibrationless parallel imaging reconstruction through learning from coil
and protocol specific data.
