将卡尔曼平滑与深度去噪结合，提升动态成像计算效率。
Efficient Plug-and-Play method for Dynamic Imaging Via Kalman Smoothing
- 用卡尔曼平滑处理状态空间模型，引入深度网络作为先验去噪器。
- 在2D+t成像任务中，相比传统方法提速显著，尤其适用于多时间步场景。
- 适合需要高效动态图像重建的研究者，如医学影像、视频恢复领域。
状态空间模型（SSM）在信号处理中广泛应用，其中卡尔曼平滑（KS）是主流方法。然而，传统KS方法缺乏空间先验信息的表达能力。最近，[1] 提出一种基于ADMM的算法，利用KS处理状态空间保真项，并通过基于稀疏性的先验和邻近算子进行物体正则化。插件式（PnP）方法是一种流行的迭代算法，用强大的去噪器（如深度神经网络）替代编码先验知识的邻近算子，广泛应用于图像处理并取得领先性能。本文在KS-ADMM基础上，结合深度学习以提升表达能力，提出一种基于KS-ADMM迭代的PnP算法，通过卡尔曼平滑高效处理状态空间模型，同时支持使用强大去噪网络。在2D+t成像问题上的仿真表明，所提出的PnP-KS-ADMM算法在大量时间步条件下，相比标准PnP-ADMM具有更高的计算效率。
原文摘要 · Abstract (English)
State-space models (SSM) are common in signal processing, where Kalman smoothing (KS) methods are state-of-the-art. However, traditional KS techniques lack expressivity as they do not incorporate spatial prior information. Recently, [1] proposed an ADMM algorithm that handles the state-space fidelity term with KS while regularizing the object via a sparsity-based prior with proximity operators. Plug-and-Play (PnP) methods are a popular type of iterative algorithms that replace proximal operators encoding prior knowledge with powerful denoisers such as deep neural networks. These methods are widely used in image processing, achieving state-of-the-art results. In this work, we build on the KS-ADMM method, combining it with deep learning to achieve higher expressivity. We propose a PnP algorithm based on KS-ADMM iterations, efficiently handling the SSM through KS, while enabling the use of powerful denoising networks. Simulations on a 2D+t imaging problem show that the proposed PnP-KS-ADMM algorithm improves the computational efficiency over standard PnP-ADMM for large numbers of timesteps.
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