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.

通过使用未经训练的神经网络（UNNs）模拟源结构，我们开发了一种理论框架来表征这些 UNN 方法的性能，同时利用最近提出的袋装深度图像先验（bagged-DIP）思想开发了快照压缩成像（SCI）袋装深度视频先验（SCI-BDVP）算法，在视频 SCI 中实现了最新技术，甚至在噪声测量情况下优于半监督解决方案。

非训练的神经网络用于快照压缩成像：理论和算法

Untrained Neural Nets for Snapshot Compressive Imaging: Theory and  Algorithms

Fourier phase retrieval (FPR) is a challenging task widely used in various
applications. It involves recovering an unknown signal from its Fourier
phaseless measurements. FPR with few measurements is important for reducing
time and hardware costs, but it suffers from serious ill-posedness. Recently,
untrained neural networks have offered new approaches by introducing learned
priors to alleviate the ill-posedness without requiring any external data.
However, they may not be ideal for reconstructing fine details in images and
can be computationally expensive. This paper proposes an untrained neural
network (NN) embedded algorithm based on the alternating direction method of
multipliers (ADMM) framework to solve FPR with few measurements. Specifically,
we use a generative network to represent the image to be recovered, which
confines the image to the space defined by the network structure. To improve
the ability to represent high-frequency information, total variation (TV)
regularization is imposed to facilitate the recovery of local structures in the
image. Furthermore, to reduce the computational cost mainly caused by the
parameter updates of the untrained NN, we develop an accelerated algorithm that
adaptively trades off between explicit and implicit regularization.
Experimental results indicate that the proposed algorithm outperforms existing
untrained NN-based algorithms with fewer computational resources and even
performs competitively against trained NN-based algorithms.

使用基于交替方向乘子方法（ADMM）框架的未训练神经网络（NN）嵌入算法，通过生成网络和总变差（TV）正则化来解决具有少量测量的 Fourier 相位恢复（FPR）问题，从而减少计算资源，并能与训练的 NN 算法竞争性地表现。

基于未经训练的神经网络的傅里叶相位恢复及其在极少测量中的嵌入

Untrained neural network embedded Fourier phase retrieval from few  measurements

We consider using {\bf\em untrained neural networks} to solve the
reconstruction problem of snapshot compressive imaging (SCI), which uses a
two-dimensional (2D) detector to capture a high-dimensional (usually 3D)
data-cube in a compressed manner. Various SCI systems have been built in recent
years to capture data such as high-speed videos, hyperspectral images, and the
state-of-the-art reconstruction is obtained by the deep neural networks.
However, most of these networks are trained in an end-to-end manner by a large
amount of corpus with sometimes simulated ground truth, measurement pairs. In
this paper, inspired by the untrained neural networks such as deep image priors
(DIP) and deep decoders, we develop a framework by integrating DIP into the
plug-and-play regime, leading to a self-supervised network for spectral SCI
reconstruction. Extensive synthetic and real data results show that the
proposed algorithm without training is capable of achieving competitive results
to the training based networks. Furthermore, by integrating the proposed method
with a pre-trained deep denoising prior, we have achieved state-of-the-art
results. {Our code is available at
https://github.com/mengziyi64/CASSI-Self-Supervised.}

本文提出了一种结合 DIP 的插入式自监督网络框架，使用未经训练的神经网络解决了快照压缩成像的光谱重建问题，实验证明该算法可以在不使用大量模拟数据的情况下取得与基于训练的网络相媲美的性能，并可与预训练的深度去噪先验结合以获得最先进的结果。