This paper focuses on the analysis of sequential image data, particularly brain imaging data such as MRI, fMRI, CT, with the motivation of understanding the brain aging process and neurodegenerative diseases. To achieve this goal, we investigate image generation in a time series context. Specifically, we formulate a min-max problem derived from the $f$-divergence between neighboring pairs to learn a time series generator in a nonparametric manner. The generator enables us to generate future images by transforming prior lag-k observations and a random vector from a reference distribution. With a deep neural network learned generator, we prove that the joint distribution of the generated sequence converges to the latent truth under a Markov and a conditional invariance condition. Furthermore, we extend our generation mechanism to a panel data scenario to accommodate multiple samples. The effectiveness of our mechanism is evaluated by generating real brain MRI sequences from the Alzheimer's Disease Neuroimaging Initiative. These generated image sequences can be used as data augmentation to enhance the performance of further downstream tasks, such as Alzheimer's disease detection.

翻译：本文聚焦于序列图像数据的分析，特别是脑成像数据（如MRI、fMRI、CT），旨在理解大脑衰老过程与神经退行性疾病。为实现这一目标，我们研究了时间序列背景下的图像生成问题。具体而言，我们基于相邻数据对之间的$f$-散度构建了一个极小极大问题，以非参数方式学习时间序列生成器。该生成器能够通过转换先前的滞后k期观测值以及来自参考分布的随机向量，生成未来图像。对于通过深度神经网络学习得到的生成器，我们证明了在满足马尔可夫性和条件不变性假设下，生成序列的联合分布收敛于潜在的真实分布。此外，我们将生成机制扩展至面板数据场景以适应多样本情况。通过使用阿尔茨海默病神经影像倡议计划的真实脑部MRI序列进行生成实验，验证了本机制的有效性。所生成的图像序列可作为数据增强材料，用于提升下游任务（如阿尔茨海默病检测）的性能。