Method for performing magnetic resonance imaging reconstruction with unsupervised deep learning

1. A method for magnetic resonance imaging comprising:

a) performing unsupervised training of a deep neural network of an MRI apparatus using a training set of under-sampled MRI scans, wherein each scan comprises slices of under-sampled, unclassified k-space MRI measurements;

b) performing by the MRI apparatus an under-sampled scan to produce under-sampled k-space data;

c) updating the deep neural network with the under-sampled scan;

d) processing the under-sampled k-space data by the updated deep neural network of the MRI apparatus to reconstruct a final MRI image;

wherein the unsupervised training of the deep neural network of the MRI apparatus using the training set of under-sampled MRI scans comprises:

i) selecting a set of training batches, where each of the training batches is a set of under-sampled slices randomly selected from the training set of under-sampled MRI scans;

ii) updating with backpropagation the deep neural network with the training batches by sequentially applying to the deep neural network the training batches, evaluating for each applied training batch an unsupervised loss function.

2. The method of claim 1 wherein the unsupervised loss function is a sum over slices in the applied training batch of a regularization term plus a difference between a slice in the applied training batch and an encoding operator applied to an image output from the deep neural network from applying the slice in the applied training batch.

3. The method of claim 2 wherein the regularization term is a sum over products of constant regularization coefficients and regularization functions of the image output from the deep neural network.

4. The method of claim 2 wherein the deep neural network comprises a set of neural network channels for processing in parallel the slices in the applied training batch, where each of the channels produces the image output from the deep neural network from applying the slice in the applied training batch, where each channel comprises a sequence of block pairs, where each of the block pairs comprises a data consistency block and a neural network block.

5. The method of claim 4 wherein the data consistency block processes the slice of the applied training batch and a prior intermediate image from a prior block pair to produce an output, and the neural network block processes the output to produce an intermediate image for a subsequent block pair, where the neural network block comprises a channel augmentation layer, multiple convolution layers, and a channel combination layer.

6. The method of claim 1 wherein the training set of under-sampled MRI scans comprises scans of more than 100 different subjects, and wherein each scan comprises at least 10 slices of under-sampled, unclassified k-space MRI measurements.