  Recent studies show that deep learning (DL) based MRI reconstruction
outperforms conventional methods, such as parallel imaging and compressed
sensing (CS), in multiple applications. Unlike CS that is typically implemented
with pre-determined linear representations for regularization, DL inherently
uses a non-linear representation learned from a large database. Another line of
work uses transform learning (TL) to bridge the gap between these two
approaches by learning linear representations from data. In this work, we
combine ideas from CS, TL and DL reconstructions to learn deep linear
convolutional transforms as part of an algorithm unrolling approach. Using
end-to-end training, our results show that the proposed technique can
reconstruct MR images to a level comparable to DL methods, while supporting
uniform undersampling patterns unlike conventional CS methods. Our proposed
method relies on convex sparse image reconstruction with linear representation
at inference time, which may be beneficial for characterizing robustness,
stability and generalizability.
