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Uncertainty Estimation and Out-of-Distribution Detection for Deep Learning-Based Image Reconstruction using the Local Lipschitz

2023-12-01 16:00:14
Danyal F. Bhutto, Bo Zhu, Jeremiah Z. Liu, Neha Koonjoo, Hongwei B. Li, Bruce R. Rosen, Matthew S. Rosen

Abstract

Accurate image reconstruction is at the heart of diagnostics in medical imaging. Supervised deep learning-based approaches have been investigated for solving inverse problems including image reconstruction. However, these trained models encounter unseen data distributions that are widely shifted from training data during deployment. Therefore, it is essential to assess whether a given input falls within the training data distribution for diagnostic purposes. Uncertainty estimation approaches exist but focus on providing an uncertainty map to radiologists, rather than assessing the training distribution fit. In this work, we propose a method based on the local Lipschitz-based metric to distinguish out-of-distribution images from in-distribution with an area under the curve of 99.94%. Empirically, we demonstrate a very strong relationship between the local Lipschitz value and mean absolute error (MAE), supported by a high Spearman's rank correlation coefficient of 0.8475, which determines the uncertainty estimation threshold for optimal model performance. Through the identification of false positives, the local Lipschitz and MAE relationship was used to guide data augmentation and reduce model uncertainty. Our study was validated using the AUTOMAP architecture for sensor-to-image Magnetic Resonance Imaging (MRI) reconstruction. We compare our proposed approach with baseline methods: Monte-Carlo dropout and deep ensembles, and further analysis included MRI denoising and Computed Tomography (CT) sparse-to-full view reconstruction using UNET architectures. We show that our approach is applicable to various architectures and learned functions, especially in the realm of medical image reconstruction, where preserving the diagnostic accuracy of reconstructed images remains paramount.

Abstract (translated)

精确的图像重建是医学影像诊断的核心。已研究了使用监督深度学习方法来解决包括图像重建在内的反问题。然而,这些训练好的模型在部署时会面临从训练数据分布广泛偏移的未见数据分布。因此,在诊断目的下评估给定输入是否落在训练数据分布非常重要。不确定性估计方法存在,但主要关注提供给放射医生的不确定性地图,而不是评估训练分布的拟合度。在这项工作中,我们提出了一种基于局部Lipschitz度量的方法来区分离散和分布中的图像。通过99.94%面积下的平均绝对误差(MAE)与局部Lipschitz值的关系,我们实验证明了一个非常强的关系。通过识别假阳性,我们利用局部Lipschitz和MAE关系指导数据增强和减少模型不确定性。我们的研究通过AUTOMAP架构对传感器到图像的磁共振成像(MRI)重建进行了验证。我们比较了我们的方法与基线方法:蒙特卡洛随机失活和深度集成,还进一步分析了使用UNET架构的CT稀疏到全视图重建。我们证明了我们的方法适用于各种架构和学习函数,尤其是在医学图像重建领域,保留重建图像的诊断准确性至关重要。

URL

https://arxiv.org/abs/2305.07618

PDF

https://arxiv.org/pdf/2305.07618.pdf


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