Equivariant neural networks for inverse problems

In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven be a very fruitful idea. The successes this approach have motivated line research into incorporating other symmetries deep learning methods, form group equivariant networks. Much work been focused on roto-translational symmetry $\mathbf R^d$, but examples are scaling R^d$ and rotational sphere. work, we demonstrate that operations can naturally incorporated learned reconstruction methods for inverse problems by variational regularisation approach. Indeed, if functional is invariant under symmetry, corresponding proximal operator will satisfy equivariance property with respect same symmetry. As result observation, design iterative which operators modelled as We roto-translationally proposed methodology apply it low-dose computerised tomography subsampled magnetic resonance imaging reconstruction. demonstrated improve quality method little extra computational cost at training time without any test time.