Plug-and-Play Priors (PnP) is a well-known class of methods for solving
inverse problems in computational imaging. PnP methods combine physical forward
models with learned prior models specified as image denoisers. A common issue
with the learned models is that of a performance drop when there is a
distribution shift between the training and testing data. Test-time training
(TTT) was recently proposed as a general strategy for improving the performance
of learned models when training and testing data come from different
distributions. In this paper, we propose PnP-TTT as a new method for overcoming
distribution shifts in PnP. PnP-TTT uses deep equilibrium learning (DEQ) for
optimizing a self-supervised loss at the fixed points of PnP iterations.
PnP-TTT can be directly applied on a single test sample to improve the
generalization of PnP. We show through simulations that given a sufficient
number of measurements, PnP-TTT enables the use of image priors trained on
natural images for image reconstruction in magnetic resonance imaging (MRI).

提出了 PnP-TTT 这种新方法来克服 PnP 方法中的分布偏移问题，通过在 PnP 迭代的固定点上优化自监督损失来应用于单个测试样本以改善 PnP 的泛化能力。模拟实验表明，在测量次数足够的情况下，PnP-TTT 可以使用在自然图像上训练的图像先验进行磁共振成像（MRI）的图像重建。

利用测试时间训练克服插拔式方法中的分布偏移

Overcoming Distribution Shifts in Plug-and-Play Methods with Test-Time  Training

Federated Learning (FL) is a prominent distributed learning paradigm
facilitating collaboration among nodes within an edge network to co-train a
global model without centralizing data. By shifting computation to the network
edge, FL offers robust and responsive edge-AI solutions and enhance
privacy-preservation. However, deploying deep FL models within edge
environments is often hindered by communication bottlenecks, data
heterogeneity, and memory limitations. To address these challenges jointly, we
introduce FeDEQ, a pioneering FL framework that effectively employs deep
equilibrium learning and consensus optimization to exploit a compact shared
data representation across edge nodes, allowing the derivation of personalized
models specific to each node. We delve into a unique model structure composed
of an equilibrium layer followed by traditional neural network layers. Here,
the equilibrium layer functions as a global feature representation that edge
nodes can adapt to personalize their local layers. Capitalizing on FeDEQ's
compactness and representation power, we present a novel distributed algorithm
rooted in the alternating direction method of multipliers (ADMM) consensus
optimization and theoretically establish its convergence for smooth objectives.
Experiments across various benchmarks demonstrate that FeDEQ achieves
performance comparable to state-of-the-art personalized methods while employing
models of up to 4 times smaller in communication size and 1.5 times lower
memory footprint during training.

FeDEQ 是一种先驱性的联邦学习框架，利用深度均衡学习和一致性优化有效地在边缘节点之间利用紧凑的共享数据表示，允许派生个性化模型，并通过采用交替方向法解（ADMM）一致性优化的新型分布式算法，理论上证明了其收敛性。实验结果表明，与最先进的个性化方法相比，FeDEQ 在通信大小上使用的模型可小 4 倍，并且在训练时内存占用更少 1.5 倍，性能可媲美。