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We present PROSUB: PROgressive SUBsampling, a deep learning based, automatedmethodology that subsamples an oversampled data set (e.g. multi-channeled 3Dimages) with minimal loss of information. We build upon a recent dual-networkapproach that won the MICCAI MUlti-DIffusion (MUDI) quantitative MRImeasurement sampling-reconstruction challenge, but suffers from deep learningtraining instability, by subsampling with a hard decision boundary. PROSUB usesthe paradigm of recursive feature elimination (RFE) and progressivelysubsamples measurements during deep learning training, improving optimizationstability. PROSUB also integrates a neural architecture search (NAS) paradigm,allowing the network architecture hyperparameters to respond to the subsamplingprocess. We show PROSUB outperforms the winner of the MUDI MICCAI challenge,producing large improvements >18% MSE on the MUDI challenge sub-tasks andqualitative improvements on downstream processes useful for clinicalapplications. We also show the benefits of incorporating NAS and analyze theeffect of PROSUB's components. As our method generalizes to other problemsbeyond MRI measurement selection-reconstruction, our code ishttps://github.com/sbb-gh/PROSUB

Progressive Subsampling for Oversampled Data - Application to Quantitative MRI