Adaptive Selection of Sampling-Reconstruction in Fourier Compressed Sensing

Compressed sensing (CS) has emerged to overcome the inefficiency of Nyquist sampling. However, traditional optimization-based reconstruction is slow and can not yield an exact image in practice. Deep learning-based reconstruction has been a promising alternative to optimization-based reconstruction, outperforming it in accuracy and computation speed. Finding an efficient sampling method with deep learning-based reconstruction, especially for Fourier CS remains a challenge. Existing joint optimization of sampling-reconstruction works (H1) optimize the sampling mask but have low potential as it is not adaptive to each data point. Adaptive sampling (H2) has also disadvantages of difficult optimization and Pareto sub-optimality. Here, we propose a novel adaptive selection of sampling-reconstruction (H1.5) framework that selects the best sampling mask and reconstruction network for each input data. We provide theorems that our method has a higher potential than H1 and effectively solves the Pareto sub-optimality problem in sampling-reconstruction by using separate reconstruction networks for different sampling masks. To select the best sampling mask, we propose to quantify the high-frequency Bayesian uncertainty of the input, using a super-resolution space generation model. Our method outperforms joint optimization of sampling-reconstruction (H1) and adaptive sampling (H2) by achieving significant improvements on several Fourier CS problems.