  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.
