Computational image reconstruction algorithms generally produce a single
image without any measure of uncertainty or confidence. Regularized Maximum
Likelihood (RML) and feed-forward deep learning approaches for inverse problems
typically focus on recovering a point estimate. This is a serious limitation
when working with underdetermined imaging systems, where it is conceivable that
multiple image modes would be consistent with the measured data. Characterizing
the space of probable images that explain the observational data is therefore
crucial. In this paper, we propose a variational deep probabilistic imaging
approach to quantify reconstruction uncertainty. Deep Probabilistic Imaging
(DPI) employs an untrained deep generative model to estimate a posterior
distribution of an unobserved image. This approach does not require any
training data; instead, it optimizes the weights of a neural network to
generate image samples that fit a particular measurement dataset. Once the
network weights have been learned, the posterior distribution can be
efficiently sampled. We demonstrate this approach in the context of
interferometric radio imaging, which is used for black hole imaging with the
Event Horizon Telescope, and compressed sensing Magnetic Resonance Imaging
(MRI).

该研究提出了一种利用未经训练的深度生成模型估计未观察图像的后验分布的方法，从而量化重建不确定性。这种方法不需要训练数据，而是优化神经网络的权重以生成适合特定测量数据集的图像样本，通过这种方法，在干涉射电成像和压缩感知磁共振成像等领域得出了实证结果。

深度概率成像：计算成像的不确定性量化与多模态解决方案表征

Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal  Solution Characterization for Computational Imaging

Generative Adversarial Networks (GANs) are powerful tools for reconstructing
Compressed Sensing Magnetic Resonance Imaging (CS-MRI). However most recent
works lack exploration of structure information of MRI images that is crucial
for clinical diagnosis. To tackle this problem, we propose the
Structure-Enhanced GAN (SEGAN) that aims at restoring structure information at
both local and global scale. SEGAN defines a new structure regularization
called Patch Correlation Regularization (PCR) which allows for efficient
extraction of structure information. In addition, to further enhance the
ability to uncover structure information, we propose a novel generator SU-Net
by incorporating multiple-scale convolution filters into each layer. Besides,
we theoretically analyze the convergence of stochastic factors contained in
training process. Experimental results show that SEGAN is able to learn target
structure information and achieves state-of-the-art performance for CS-MRI
reconstruction.

通过使用新的结构正则化技术和多尺度的卷积滤波器，我们提出了 SEGAN 和 SU-Net 来增强 CS-MRI 图像的结构信息，实验结果表明其能够学习目标结构信息并取得了最先进的性能。