Research shows that deep learning (DL) based MRI reconstruction outperform conventional methods, such as parallel imaging and compressed sensing (CS). Unlike CS with pre-determined linear representations for regularization, DL uses nonlinear representations learned from a large database. Transform learning (TL) is another line of work bridging the gap between these two approaches. In this work, we combine ideas from CS, TL and DL to learn deep linear convolutional transforms, which has comparable performance to DL and supports uniform under-sampling unlike CS, while enabling sparse convex optimization at inference time.
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