We present Posterior Temperature Optimized Bayesian Inverse Models (POTOBIM), an unsupervised Bayesian approach to inverse problems in medical imaging using mean-field variational inference with a fully tempered posterior. Bayesian methods exhibit useful properties for approaching inverse tasks, such as tomographic reconstruction or image denoising. A suitable prior distribution introduces regularization, which is needed to solve the ill-posed problem and reduces overfitting the data. In practice, however, this often results in a suboptimal posterior temperature, and the full potential of the Bayesian approach is not being exploited. In POTOBIM, we optimize both the parameters of the prior distribution and the posterior temperature with respect to reconstruction accuracy using Bayesian optimization with Gaussian process regression. Our method is extensively evaluated on four different inverse tasks on a variety of modalities with images from public data sets and we demonstrate that an optimized posterior temperature outperforms both non-Bayesian and Bayesian approaches without temperature optimization. The use of an optimized prior distribution and posterior temperature leads to improved accuracy and uncertainty estimation and we show that it is sufficient to find these hyperparameters per task domain. Well-tempered posteriors yield calibrated uncertainty, which increases the reliability in the predictions. Our source code is publicly available at github.com/Cardio-AI/mfvi-dip-mia.

翻译：我们展示了波氏温度优化巴耶斯反贝氏模型(POTOBIM),这是一种不受监督的巴耶斯人方法,用中场变异性推断法处理医学成像中的逆向问题。巴伊西亚方法展示了处理反向任务(如图象重建或图像脱色)的有用性。适当的先前分配方法引入了正规化,这是解决错误问题和减少数据过度所需的。但在实践中,这往往导致亚贝斯人方法的次优性后温,而巴伊西亚方法的全部潜力没有被利用。在POTOBIM中,我们优化了先前分布的参数和后台温度的参数,利用巴伊斯人优化后台的优化后台的精确度,使用巴伊斯的优化前台的精确度和后台的精确度来进行重建。我们的方法在四种不同方式上进行了广泛的反向评估,这些方式包括公共数据集的图像,我们证明,最优化的后台温度超越非巴耶斯和拜亚斯人方法,而没有温度调整。在最佳前台的预测和后台的精确度中,我们利用了最精确度的模型的精确度,在海平地平面的精确度上显示我们每台的精确度上,我们每个的精确度上都显示。