cs.CV提交于 2026-11-02已译

从噪声测量中学习干净的生成过程

Learning Clean Generative Processes from Noisy Measurements

Fabian Kruse · Lorenzo Baldassari · Ivan Dokmani\'c

中文摘要

研究仅用噪声观测学习干净图像生成模型的问题。扩散过程及其对非高斯噪声的推广需要在每个噪声水平上做后验预测。首先证明，可用 Noise2Noise 回归从独立噪声视图学习这些预测，但仅限训练数据噪声水平及以上。为学习生成干净图像所需的更低噪声水平预测，引入一致性约束：预测应等于继续采样过程后的期望。推导出一致性唯一确定向干净图像分布延续的条件，并在 Poisson、binomial、Gamma 和 negative-binomial 测量上验证。在 CIFAR-10、光子计数显微和合成孔径雷达上的实验表明，所需后验预测可仅从噪声视图学习，且一致性关系能修复超出数据噪声水平的延续，而无一致性时该延续严重退化。

关键要点

01问题：仅用噪声观测学习干净图像生成模型，低噪声水平后验预测难以获得
02方法：用 Noise2Noise 回归学习预测，并加一致性约束延续到干净分布
03结果：在 Poisson、binomial、Gamma、negative-binomial 测量上验证一致性条件
04结果：CIFAR-10、光子计数显微和合成孔径雷达实验验证方法有效
05局限：Noise2Noise 回归仅能在训练数据噪声水平及以上学习预测

解读

尚无解读。

原始英文摘要

arXiv:2610.42036v1 Announce Type: cross Abstract: We study how to learn a generative model of clean images using only noisy observations. Diffusion processes and their generalizations to non-Gaussian noise require posterior predictions at every noise level. We first show that it is possible to learn these predictions from independent noisy views using Noise2Noise regression, but only at or above the noise level of the training data. To learn the predictions below that level, needed to generate clean images, we impose consistency: a prediction should equal its expectation after continuing the sampling process. We derive conditions under which consistency uniquely determines the continuation to the clean image distribution and verify them for Poisson, binomial, Gamma, and negative-binomial measurements. Experiments on CIFAR-10, photon-counting microscopy, and synthetic aperture radar show that the required posterior predictions can be learned from noisy views alone and that the consistency relation repairs the continuation beyond the noise level of the data, which severely deteriorates without consistency.