Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements (2111.12855v2)

Abstract: Deep networks provide state-of-the-art performance in multiple imaging inverse problems ranging from medical imaging to computational photography. However, most existing networks are trained with clean signals which are often hard or impossible to obtain. Equivariant imaging (EI) is a recent self-supervised learning framework that exploits the group invariance present in signal distributions to learn a reconstruction function from partial measurement data alone. While EI results are impressive, its performance degrades with increasing noise. In this paper, we propose a Robust Equivariant Imaging (REI) framework which can learn to image from noisy partial measurements alone. The proposed method uses Stein's Unbiased Risk Estimator (SURE) to obtain a fully unsupervised training loss that is robust to noise. We show that REI leads to considerable performance gains on linear and nonlinear inverse problems, thereby paving the way for robust unsupervised imaging with deep networks. Code is available at: https://github.com/edongdongchen/REI.

• The paper introduces the REI framework which leverages SURE-based unsupervised loss to reconstruct images from noisy and partial measurements.
• Methodologically, REI refines equivariant imaging by integrating noise-adaptive losses to enhance reconstruction quality in CT, MRI, and inpainting tasks.
• Empirical results show that REI achieves up to a 7 dB improvement over traditional methods in high-noise MRI scenarios, closely approaching supervised performance.

Robust Equivariant Imaging: A Fully Unsupervised Framework for Learning to Image from Noisy and Partial Measurements

The research paper titled "Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements" introduces a noteworthy advancement in the field of imaging inverse problems by proposing a novel framework—Robust Equivariant Imaging (REI). The intricate objective of this paper is to ameliorate the limitations of existing self-supervised learning techniques that are susceptible to degradation in noisy environments, specifically within the context of imaging inverse problems such as MRI, CT, and image inpainting.

Inverse problems are a cornerstone in signal processing and computer vision, especially in applications involving computed tomography (CT), magnetic resonance imaging (MRI), and super-resolution tasks. Traditional methodologies apply prior knowledge, including sparsity and total variation, to regularize reconstructions, while recent trends have pivoted towards learning-based approaches that map noisy measurements to clean reconstructions. However, acquiring such clean signals for training is often impractical due to cost and logistics.

The paper addresses the performance limitations of the Equivariant Imaging (EI) framework, which deteriorates in accuracy as noise levels in measurements increase. The EI framework exploits group invariance within signal distributions to reconstruct images from partial data, leveraging transformation invariance properties. Despite its previous successes in noiseless scenarios, EI's efficacy diminishes rapidly in noisy contexts, necessitating a robust enhancement to maintain performance integrity.

By integrating Stein's Unbiased Risk Estimator (SURE), the proposed REI framework introduces an unsupervised training loss that effectively estimates the mean squared error (MSE) without the need for ground truth data. This innovation is pivotal as it enables the REI framework to robustly learn from noisy partial measurements alone across various noise models, including Gaussian, Poisson, and mixed Poisson-Gaussian noise. The architecture-agnostic nature of the REI methodology allows it to be adapted across a spectrum of neural network designs, facilitating its deployment in diverse imaging scenarios.

Empirical evaluations demonstrate REI's superiority over existing EI approaches and its close performance proximity to supervised learning methods, which benefit from ground truth data access. The evaluation reveals significant improvements in reconstruction quality for tasks such as sparse-view CT, accelerated MRI, and image inpainting, underscoring REI's robustness to noise and partial data incompleteness. Particularly notable is the REI's approximately 7 dB performance gain over EI in high-noise scenarios for MRI tasks, highlighting its substantial advantage in challenging conditions.

The inclusion of unsupervised learning methods utilizing SURE-based noise-adaptive losses extends beyond previous applications limited to models assuming full measurement availability. Notably, the paper discerns the effective blend of equivariance and noise robustness in improving unsupervised neural network-driven imaging solutions. This insight into REI's efficacy positions it as a promising alternative for imaging tasks where acquiring large datasets of clean and noisy measurement pairs is infeasible, marking a substantial stride in the evolution of deep network approaches to solving complex inverse problems.

In conclusion, the research encapsulated in this paper elucidates the potential of REI as a transformative approach in imaging inverse problem areas, delivering on the need for unsupervised methods capable of high fidelity reconstruction from incomplete and noisy data. As the field advances, the implications of such robust frameworks are profound, with direct impacts on computational efficiency and accessibility in practical imaging applications. Future investigations may explore extended applications, optimization strategies, and further theoretical substantiation of REI's performance in varied noise and data conditions.