Snapshot compressive imaging (SCI) recovers high-dimensional (3D) data cubes from a single 2D measurement, enabling diverse applications like video and hyperspectral imaging to go beyond standard techniques in terms of acquisition speed and efficiency. In this paper, we focus on SCI recovery algorithms that employ untrained neural networks (UNNs), such as deep image prior (DIP), to model source structure. Such UNN-based methods are appealing as they have the potential of avoiding the computationally intensive retraining required for different source models and different measurement scenarios. We first develop a theoretical framework for characterizing the performance of such UNN-based methods. The theoretical framework, on the one hand, enables us to optimize the parameters of data-modulating masks, and on the other hand, provides a fundamental connection between the number of data frames that can be recovered from a single measurement to the parameters of the untrained NN. We also employ the recently proposed bagged-deep-image-prior (bagged-DIP) idea to develop SCI Bagged Deep Video Prior (SCI-BDVP) algorithms that address the common challenges faced by standard UNN solutions. Our experimental results show that in video SCI our proposed solution achieves state-of-the-art among UNN methods, and in the case of noisy measurements, it even outperforms supervised solutions.

翻译：快照压缩成像（SCI）从单次二维测量中恢复高维（三维）数据立方体，使得视频和高光谱成像等多样化应用在采集速度与效率方面超越标准技术。本文聚焦于采用无训练神经网络（如深度图像先验）建模源结构的SCI恢复算法。此类基于UNN的方法具有吸引力，因为它们有望避免针对不同源模型和不同测量场景所需的计算密集型重复训练。我们首先构建了一个理论框架，用于表征此类基于UNN方法的性能。该理论框架一方面使我们能够优化数据调制掩模的参数，另一方面为单次测量可恢复的数据帧数量与无训练神经网络参数之间建立了根本性联系。我们还采用最新提出的袋装深度图像先验思想，开发了SCI袋装深度视频先验算法，以解决标准UNN方案面临的常见挑战。实验结果表明，在视频SCI任务中，我们提出的解决方案在UNN方法中达到了最优水平，且在含噪测量情况下甚至超越了有监督解决方案。