Model-based deep learning methods such as \emph{loop unrolling} (LU) and
\emph{deep equilibrium model} (DEQ) extensions offer outstanding performance in
solving inverse problems (IP). These methods unroll the optimization iterations
into a sequence of neural networks that in effect learn a regularization
function from data. While these architectures are currently state-of-the-art in
numerous applications, their success heavily relies on the accuracy of the
forward model. This assumption can be limiting in many physical applications
due to model simplifications or uncertainties in the apparatus. To address
forward model mismatch, we introduce an untrained forward model residual block
within the model-based architecture to match the data consistency in the
measurement domain for each instance. We propose two variants in well-known
model-based architectures (LU and DEQ) and prove convergence under mild
conditions. The experiments show significant quality improvement in removing
artifacts and preserving details across three distinct applications,
encompassing both linear and nonlinear inverse problems. Moreover, we highlight
reconstruction effectiveness in intermediate steps and showcase robustness to
random initialization of the residual block and a higher number of iterations
during evaluation.

基于模型的深度学习方法在解决逆问题方面表现出色，然而前向模型的准确性对于物理应用来说是有限制的。为了解决这个问题，我们在基于模型的架构中引入一个未训练的前向模型残差块来匹配每个实例在测量域中的数据一致性，我们提出了两个变体，并证明了在温和条件下的收敛性。实验结果显示，在去除伪影并保留细节方面，我们的方法在三个不同应用中都取得了显著的质量改进，涵盖了线性和非线性逆问题。此外，我们突出了中间步骤的重建效果，并展示了对于残差块的随机初始化和更多迭代次数在评估中的稳健性。

利用基于模型的结构中未训练的神经网络解决具有模型不匹配的逆问题

Solving Inverse Problems with Model Mismatch using Untrained Neural  Networks within Model-based Architectures

There is a growing interest in model-based deep learning (MBDL) for solving
imaging inverse problems. MBDL networks can be seen as iterative algorithms
that estimate the desired image using a physical measurement model and a
learned image prior specified using a convolutional neural net (CNNs). The
iterative nature of MBDL networks increases the test-time computational
complexity, which limits their applicability in certain large-scale
applications. We address this issue by presenting structured pruning algorithm
for model-based deep learning (SPADE) as the first structured pruning algorithm
for MBDL networks. SPADE reduces the computational complexity of CNNs used
within MBDL networks by pruning its non-essential weights. We propose three
distinct strategies to fine-tune the pruned MBDL networks to minimize the
performance loss. Each fine-tuning strategy has a unique benefit that depends
on the presence of a pre-trained model and a high-quality ground truth. We
validate SPADE on two distinct inverse problems, namely compressed sensing MRI
and image super-resolution. Our results highlight that MBDL models pruned by
SPADE can achieve substantial speed up in testing time while maintaining
competitive performance.

通过引入结构修剪算法（SPADE）来降低计算复杂性，从而实现基于模型的深度学习网络（MBDL）在大规模应用中的可适用性。

基于模型的深度学习的结构化剪枝算法

A Structured Pruning Algorithm for Model-based Deep Learning

Model-based deep learning solutions to inverse problems have attracted
increasing attention in recent years as they bridge state-of-the-art numerical
performance with interpretability. In addition, the incorporated prior domain
knowledge can make the training more efficient as the smaller number of
parameters allows the training step to be executed with smaller datasets.
Algorithm unrolling schemes stand out among these model-based learning
techniques. Despite their rapid advancement and their close connection to
traditional high-dimensional statistical methods, they lack certainty estimates
and a theory for uncertainty quantification is still elusive. This work
provides a step towards closing this gap proposing a rigorous way to obtain
confidence intervals for the LISTA estimator.

提供获取 LISTA 估计器置信区间的一种严格方法，弥补了模型基础学习技术中缺乏确定性估计和不确定性量化理论方面的差距。

学习 ISTA 的不确定性量化

Uncertainty quantification for learned ISTA

Model-based deep learning has achieved astounding successes due in part to
the availability of large-scale real-world data. However, processing such
massive amounts of data comes at a considerable cost in terms of computations,
storage, training and the search for good neural architectures. Dataset
distillation has thus recently come to the fore. This paradigm involves
distilling information from large real-world datasets into tiny and compact
synthetic datasets such that processing the latter ideally yields similar
performances as the former. State-of-the-art methods primarily rely on learning
the synthetic dataset by matching the gradients obtained during training
between the real and synthetic data. However, these gradient-matching methods
suffer from the so-called accumulated trajectory error caused by the
discrepancy between the distillation and subsequent evaluation. To mitigate the
adverse impact of this accumulated trajectory error, we propose a novel
approach that encourages the optimization algorithm to seek a flat trajectory.
We show that the weights trained on synthetic data are robust against the
accumulated errors perturbations with the regularization towards the flat
trajectory. Our method, called Flat Trajectory Distillation (FTD), is shown to
boost the performance of gradient-matching methods by up to 4.7% on a subset of
images of the ImageNet dataset with higher resolution images. We also validate
the effectiveness and generalizability of our method with datasets of different
resolutions and demonstrate its applicability to neural architecture search.
Code is available at this https URL.

本文提出了一种基于优化算法的 Flat Trajectory Distillation（FTD）方法来缓解 distortion 和 subsequent evaluation 之间的累积轨迹误差，实验证明该方法可提高梯度匹配方法的性能，并适用于神经架构搜索。