Jérémy Scanvic

Jérémy Scanvic, Quentin Barthélemy, Julián Tachella

The simplicity and effectiveness of the UNet architecture makes it ubiquitous in image restoration, image segmentation, and diffusion models. They are often assumed to be equivariant to translations, yet they traditionally consist of layers that are known to be prone to aliasing, which hinders their equivariance in practice. To overcome this limitation, we propose a new alias-free UNet designed from a careful selection of state-of-the-art translation-equivariant layers. We evaluate the proposed equivariant architecture against non-equivariant baselines on image restoration tasks and observe competitive performance with a significant increase in measured equivariance. Through extensive ablation studies, we also demonstrate that each change is crucial for its empirical equivariance. Our implementation is available at https://github.com/jscanvic/UNet-AF

Jérémy Scanvic, Mike Davies, Patrice Abry et al.

Self-supervised methods have recently proved to be nearly as effective as supervised ones in various imaging inverse problems, paving the way for learning-based approaches in scientific and medical imaging applications where ground truth data is hard or expensive to obtain. 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 roto-translations is insufficient to learn from measurements that only contain low-frequency information. Instead, we propose scale-equivariant imaging, a new self-supervised approach that leverages the fact that many image distributions are approximately scale-invariant, enabling the recovery of high-frequency information 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.

Victor Sechaud, Jérémy Scanvic, Quentin Barthélemy et al.

Self-supervised learning for inverse problems allows to train a reconstruction network from noise and/or incomplete data alone. These methods have the potential of enabling learning-based solutions when obtaining ground-truth references for training is expensive or even impossible. In this paper, we propose a new self-supervised learning strategy devised for the challenging setting where measurements are observed via a single incomplete observation model. We introduce a new definition of equivariance in the context of reconstruction networks, and show that the combination of self-supervised splitting losses and equivariant reconstruction networks results in the same minimizer in expectation as the one of a supervised loss. Through a series of experiments on image inpainting, accelerated magnetic resonance imaging, and compressive sensing, we demonstrate that the proposed loss achieves state-of-the-art performance in settings with highly rank-deficient forward models.