The solution of inverse problems is of fundamental interest in medical and
astronomical imaging, geophysics as well as engineering and life sciences.
Recent advances were made by using methods from machine learning, in particular
deep neural networks. Most of these methods require a huge amount of (paired)
data and computer capacity to train the networks, which often may not be
available. Our paper addresses the issue of learning from small data sets by
taking patches of very few images into account. We focus on the combination of
model-based and data-driven methods by approximating just the image prior, also
known as regularizer in the variational model. We review two methodically
different approaches, namely optimizing the maximum log-likelihood of the patch
distribution, and penalizing Wasserstein-like discrepancies of whole empirical
patch distributions. From the point of view of Bayesian inverse problems, we
show how we can achieve uncertainty quantification by approximating the
posterior using Langevin Monte Carlo methods. We demonstrate the power of the
methods in computed tomography, image super-resolution, and inpainting. Indeed,
the approach provides also high-quality results in zero-shot super-resolution,
where only a low-resolution image is available. The paper is accompanied by a
GitHub repository containing implementations of all methods as well as data
examples so that the reader can get their own insight into the performance.

借助深度神经网络，本文研究了解决小数据集的逆问题，集中在将基于模型的方法与数据驱动方法相结合，通过逼近图像先验对全局经验分布的 Wasserstein 差异进行判罚及最大对数似然进行最优化，实现了贝叶斯逆问题的不确定性量化，并在计算机断层摄影、图像超分辨率和修复领域取得了高质量的结果。

小数据集学习：图像重建中的基于图块的正则化器

Learning from small data sets: Patch-based regularizers in inverse  problems for image reconstruction

Learning from small data sets is critical in many practical applications
where data collection is time consuming or expensive, e.g., robotics, animal
experiments or drug design. Meta learning is one way to increase the data
efficiency of learning algorithms by generalizing learned concepts from a set
of training tasks to unseen, but related, tasks. Often, this relationship
between tasks is hard coded or relies in some other way on human expertise. In
this paper, we frame meta learning as a hierarchical latent variable model and
infer the relationship between tasks automatically from data. We apply our
framework in a model-based reinforcement learning setting and show that our
meta-learning model effectively generalizes to novel tasks by identifying how
new tasks relate to prior ones from minimal data. This results in up to a 60%
reduction in the average interaction time needed to solve tasks compared to
strong baselines.

利用层级潜变量模型，自动推断任务之间的关系并应用于模型强化学习中，从而实现在小规模数据集上的元学习，有效提高数据利用率，解决新任务的平均交互时间缩短高达 60%。