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 ( \(\mathcal {H}_1\) ) optimize the sampling mask but yield suboptimal results because 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 lower infimum of the true risk compared to \(\mathcal {H}_1\) 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.