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The authors use a baseline 2D CNN (Efficient subpixel-shifted convolutional network, CVPR 2016) and extend it to 3D volumes (3D-ESPCN).\n+\n+![](/deep-learning/images/dmri-sr-uncertainty/figure1.png)\n+\n+NOTE: Instead of upsampling a LR image and refining it thorugh the CNN, the LR image is directly processed and the last feature maps are combined to produce a HR image (*learned interpolation*).\n+\n+**Computational cost is reduced and there no loss of information from upsampling the LR image before processing**\n+\n+A receptive field of 5x5x5 is used to predict 1x1x1 feature maps (resulting in a 2x2x2 HR patch in the final image after shuffling).\n+\n+The network is *in theory* trained using L2 reconstruction.\n+\n+\n+### Uncertainty estimation\n+\n+The authors address 2 types of uncertainty:\n+- Intrinsic uncertainty (variance of the statistical mapping from LR to HR, aka one-to-many problem; independent of the amount of training data)\n+- Parameter uncertainty (ambiguity in model parameters)\n+\n+\n+**Intrinsic uncertainty**\n+\n+Minimising a mean squared error is equivalent to minimising the NLL under a Gaussian noise 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