Encoder-decoder convolutional neural networks (CNN) have been extensively used for various inverse problems. However, their prediction error for unseen test data is difficult to estimate a priori, since the neural networks are trained using only selected data and their architectures are largely considered blackboxes. This poses a fundamental challenge in improving the performance of neural networks. Recently, it was shown that Stein's unbiased risk estimator (SURE) can be used as an unbiased estimator of the prediction error for denoising problems. However, the computation of the divergence term in SURE is difficult to implement in a neural network framework, and the condition to avoid trivial identity mapping is not well defined. In this paper, inspired by the finding that an encoderdecoder CNN can be expressed as a piecewise linear representation, we provide a close form expression of the unbiased estimator for the prediction error. The close form representation leads to a novel bootstrap and aggregation scheme to prevent a neural network from converging to an identity mapping so that it can enhance the performance. Experimental results show that the proposed algorithm provides consistent improvement in various inverse problems.
1. Summary
The authors address the problem of efficiently employing the SURE estimator as a network training regularizer. They show that for CNN autoencoders this can be efficiently computed. Their other contribution is a bagging/boosting technique which is proved to avoid trivial solutions. The proposed architecture, motivated by the theoretical statements, is shown to outperform classic and 2019 state of the art image reconstruction algorithms in MRI and EDX.
2. Decision and arguments
Unfortunately this paper is outside my expertise so I can’t evaluate the novelty of the theoretical accomplishments. However taking that as a given, they well-motive the proposed architecture and achieve impressive experimental results. The experiments are well described.
3. Questions 
a) Why do Table 1 and Figure 3 provide different PSNR and SSIM values?
b) Is there any way to measure accuracy to ground-truth with the EDX data? Or are the results just qualitative? 
c) With respect to Figure 2, and in general for autoencoders, the input and output have the same dimension. So how do you reconcile this with undersampled MRI and EDX data? I understand you train on fully sampled data—then how do you input undersampled data? Are the unknown samples set to zero?