Adaptive Selection of Sampling-Reconstruction in Fourier Compressed Sensing

Abstract

Compressed sensing (CS) has emerged to overcome the inefficiency of Nyquist sampling. However, traditional optimization-based reconstruction is slow and may not yield a high-quality 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 yield suboptimal results because 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 lower infimum of the true risk compared to 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.