DeepInverse: A Python package for solving imaging inverse problems with deep learning

DeepInverse is an open-source PyTorch-based library for solving imaging inverse problems. The library covers all crucial steps in image reconstruction from the efficient implementation of forward operators (e.g., optics, MRI, tomography), to the definition and resolution of variational problems and the design and training of advanced neural network architectures. In this paper, we describe the main functionality of the library and discuss the main design choices.

Translation-Equivariance of Normalization Layers and Aliasing in Convolutional Neural Networks

The design of convolutional neural architectures that are exactly equivariant to continuous translations is an active field of research. It promises to benefit scientific computing, notably by making existing imaging systems more physically accurate. Most efforts focus on the design of downsampling/pooling layers, upsampling layers and activation functions, but little attention is dedicated to normalization layers. In this work, we present a novel theoretical framework for understanding the equivariance of normalization layers to discrete shifts and continuous translations. We also determine necessary and sufficient conditions for normalization layers to be equivariant in terms of the dimensions they operate on. Using real feature maps from ResNet-18 and ImageNet, we test those theoretical results empirically and find that they are consistent with our predictions.

Self-Supervised Learning for Image Super-Resolution and Deblurring

Self-supervised methods have recently proved to be nearly as effective as supervised methods in various imaging inverse problems, paving the way for learning-based methods in scientific and medical imaging applications where ground truth data is hard or expensive to obtain. This is the case in magnetic resonance imaging and computed tomography. These methods critically rely on invariance to translations and/or rotations of the image distribution to learn from incomplete measurement data alone. However, existing approaches fail to obtain competitive performances in the problems of image super-resolution and deblurring, which play a key role in most imaging systems. In this work, we show that invariance to translations and rotations is insufficient to learn from measurements that only contain low-frequency information. Instead, we propose a new self-supervised approach that leverages the fact that many image distributions are approximately scale-invariant, and that can be applied to any inverse problem where high-frequency information is lost in the measurement process. We demonstrate throughout a series of experiments on real datasets that the proposed method outperforms other self-supervised approaches, and obtains performances on par with fully supervised learning.