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Convolutional neural networks lack shift equivariance due to the presence ofdownsampling layers. In image classification, adaptive polyphase downsampling(APS-D) was recently proposed to make CNNs perfectly shift invariant. However,in networks used for image reconstruction tasks, it can not by itself restoreshift equivariance. We address this problem by proposing adaptive polyphaseupsampling (APS-U), a non-linear extension of conventional upsampling, whichallows CNNs with symmetric encoder-decoder architecture (for example U-Net) toexhibit perfect shift equivariance. With MRI and CT reconstruction experiments,we show that networks containing APS-D/U layers exhibit state of the artequivariance performance without sacrificing on image reconstruction quality.In addition, unlike prior methods like data augmentation and anti-aliasing, thegains in equivariance obtained from APS-D/U also extend to images outside thetraining distribution.

Truly shift-equivariant convolutional neural networks with adaptive polyphase upsampling