The limited angle Radon transform is notoriously difficult to invert due to
the ill-posedness. In this work, we give a mathematical explanation that the
data-driven approach based on deep neural networks can reconstruct more
information in a stable way compared to traditional methods.

基于深度神经网络的数据驱动方法相较于传统方法，能够更稳定地重建有限角度 Radon 变换中的信息。

有限角度层析成像中的数据驱动方法的鲁棒性

Robustness of the data-driven approach in limited angle tomography

Deep Neural Networks (DNNs) demonstrated remarkable capabilities in learning
complex hierarchical data representations, but the nature of these
representations remains largely unknown. Existing global explainability
methods, such as Network Dissection, face limitations such as reliance on
segmentation masks, lack of statistical significance testing, and high
computational demands. We propose Inverse Recognition (INVERT), a scalable
approach for connecting learned representations with human-understandable
concepts by leveraging their capacity to discriminate between these concepts.
In contrast to prior work, INVERT is capable of handling diverse types of
neurons, exhibits less computational complexity, and does not rely on the
availability of segmentation masks. Moreover, INVERT provides an interpretable
metric assessing the alignment between the representation and its corresponding
explanation and delivering a measure of statistical significance, emphasizing
its utility and credibility. We demonstrate the applicability of INVERT in
various scenarios, including the identification of representations affected by
spurious correlations, and the interpretation of the hierarchical structure of
decision-making within the models.

我们提出了一种逆向识别方法 (INVERT)，通过利用学习表示与人可理解的概念之间的区分能力，实现了将学习表示与其对应解释相连接的可扩展方法。此方法具有较低的计算复杂度并且不依赖于分割掩码的可用性，还提供了一个可解释的度量来评估表示与其相应解释之间的一致性并提供统计显著性的度量值，强调其实用性和可信度。我们展示了 INVERT 在各种场景中的适用性，包括识别受偶然相关性影响的表示以及对模型中决策层次结构的解释。