Adaptive Selection of Sampling-Reconstruction in Fourier Compressed Sensing
This work addresses the problem of slow and non-adaptive sampling-reconstruction in Fourier compressed sensing for applications like medical imaging, though it appears incremental as it builds on prior joint optimization and adaptive sampling approaches.
The paper tackles the challenge of finding efficient sampling methods with deep learning-based reconstruction in Fourier compressed sensing, proposing an adaptive selection framework that chooses the best sampling mask and reconstruction network for each input data, resulting in significant improvements over existing methods on several problems.
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 ($\mathcal{H}_1$) optimize the sampling mask but have low potential as it is not adaptive to each data point. Adaptive sampling ($\mathcal{H}_2$) has also disadvantages of difficult optimization and Pareto sub-optimality. Here, we propose a novel adaptive selection of sampling-reconstruction ($\mathcal{H}_{1.5}$) 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 $\mathcal{H}_1$ 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 ($\mathcal{H}_1$) and adaptive sampling ($\mathcal{H}_2$) by achieving significant improvements on several Fourier CS problems.