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 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 (H_1) optimize the sampling mask but have low potential as it is not adaptive to each data point. Adaptive sampling (H_2) has also disadvantages of difficult optimization and Pareto sub-optimality. Here, we propose a novel adaptive selection of sampling-reconstruction (H_1.5) 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 H_1 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 (H_1) and adaptive sampling (H_2) by achieving significant improvements on several Fourier CS problems.

Tasks

Reproductions