Adaptive Selection of Sampling-Reconstruction in Fourier Compressed Sensing

• URL: http://arxiv.org/abs/2409.11738v2
• Date: Thu, 19 Sep 2024 03:54:58 GMT
• Title: Adaptive Selection of Sampling-Reconstruction in Fourier Compressed Sensing
• Authors: Seongmin Hong, Jaehyeok Bae, Jongho Lee, Se Young Chun,
• Abstract summary: Compressed sensing (CS) has emerged to overcome the inefficiency of Nyquist sampling. Deep learning-based reconstruction has been a promising alternative to optimization-based reconstruction.
• Score: 13.775902519100075
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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 ($\mathcal{H}_1$) 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.

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