  We present PROSUB: PROgressive SUBsampling, a deep learning based, automated
methodology that subsamples an oversampled data set (e.g. multi-channeled 3D
images) with minimal loss of information. We build upon a recent dual-network
approach that won the MICCAI MUlti-DIffusion (MUDI) quantitative MRI
measurement sampling-reconstruction challenge, but suffers from deep learning
training instability, by subsampling with a hard decision boundary. PROSUB uses
the paradigm of recursive feature elimination (RFE) and progressively
subsamples measurements during deep learning training, improving optimization
stability. PROSUB also integrates a neural architecture search (NAS) paradigm,
allowing the network architecture hyperparameters to respond to the subsampling
process. We show PROSUB outperforms the winner of the MUDI MICCAI challenge,
producing large improvements >18% MSE on the MUDI challenge sub-tasks and
qualitative improvements on downstream processes useful for clinical
applications. We also show the benefits of incorporating NAS and analyze the
effect of PROSUB's components. As our method generalizes to other problems
beyond MRI measurement selection-reconstruction, our code is
https://github.com/sbb-gh/PROSUB
