标题： 注入测量信息的基于扩散的逆问题求解器具有快速和噪声鲁棒性 显示英文标题

标题： Injecting Measurement Information Yields a Fast and Noise-Robust Diffusion-Based Inverse Problem Solver

摘要： 扩散模型已被确立为线性和非线性逆问题的原理性零样本求解器，这得益于它们强大的图像先验和迭代采样算法。 这些方法通常依赖于Tweedie公式，该公式将扩散变量$\mathbf{x}_t$与后验均值$\mathbb{E} [\mathbf{x}_0 | \mathbf{x}_t]$相关联，以利用最终去噪样本的估计来引导扩散轨迹$\mathbf{x}_0$。 然而，这并未考虑来自测量值$\mathbf{y}$的信息，这些信息必须在后续进行整合。 在本工作中，我们提出估计条件后验均值$\mathbb{E} [\mathbf{x}_0 | \mathbf{x}_t, \mathbf{y}]$，这可以表述为一个轻量级、单参数的最大似然估计问题的解。 由此得到的预测可以集成到任何标准采样器中，从而得到一个快速且内存高效的逆问题求解器。 我们的优化器适用于一种基于似然的噪声感知停止准则，该准则对$\mathbf{y}$中的测量噪声具有鲁棒性。 我们在多个数据集和任务上与广泛的选择的现代逆问题求解器进行了比较，表现出相当或改进的性能。 显示英文摘要

摘要： Diffusion models have been firmly established as principled zero-shot solvers for linear and nonlinear inverse problems, owing to their powerful image prior and iterative sampling algorithm. These approaches often rely on Tweedie's formula, which relates the diffusion variate $\mathbf{x}_t$ to the posterior mean $\mathbb{E} [\mathbf{x}_0 | \mathbf{x}_t]$, in order to guide the diffusion trajectory with an estimate of the final denoised sample $\mathbf{x}_0$. However, this does not consider information from the measurement $\mathbf{y}$, which must then be integrated downstream. In this work, we propose to estimate the conditional posterior mean $\mathbb{E} [\mathbf{x}_0 | \mathbf{x}_t, \mathbf{y}]$, which can be formulated as the solution to a lightweight, single-parameter maximum likelihood estimation problem. The resulting prediction can be integrated into any standard sampler, resulting in a fast and memory-efficient inverse solver. Our optimizer is amenable to a noise-aware likelihood-based stopping criteria that is robust to measurement noise in $\mathbf{y}$. We demonstrate comparable or improved performance against a wide selection of contemporary inverse solvers across multiple datasets and tasks.