用少量干净样本修复有损测量数据分布，提升恢复精度。
SFBD-OMNI: Bridge models for lossy measurement restoration with limited clean samples
- 基于单边熵最优传输构建迭代算法，处理噪声观测
- 仅需少量干净样本即可显著提升分布恢复效果
- 适用于非高斯等任意测量模型，通用性强
在许多实际场景中，获取完整观测样本成本高昂甚至不可行，而部分且含噪的观测则易于收集。本文研究在拥有大量噪声样本、且已知退化过程为黑盒生成器的前提下，如何恢复真实分布。我们证明该问题可建模为单边熵最优传输，并通过类似期望最大化（EM）的算法求解。进一步提出一种测试准则，判断在逐样本信息丢失条件下真实分布是否可恢复；若不可恢复，少量干净样本即可使分布基本恢复。基于此，我们提出SFBD-OMNI框架，通过桥接模型将受损样本分布映射至真实分布。本方法扩展了鲁棒前向-后向去卷积（SFBD；Lu et al., 2025），适用于除高斯噪声外任意测量模型。在多个基准数据集与多样测量设置下实验表明，本方法在定性与定量性能上均有显著提升。
原文摘要 · Abstract (English)
In many real-world scenarios, obtaining fully observed samples is prohibitively expensive or even infeasible, while partial and noisy observations are comparatively easy to collect. In this work, we study distribution restoration with abundant noisy samples, assuming the corruption process is available as a black-box generator. We show that this task can be framed as a one-sided entropic optimal transport problem and solved via an EM-like algorithm. We further provide a test criterion to determine whether the true underlying distribution is recoverable under per-sample information loss, and show that in otherwise unrecoverable cases, a small number of clean samples can render the distribution largely recoverable. Building on these insights, we introduce SFBD-OMNI, a bridge model-based framework that maps corrupted sample distributions to the ground-truth distribution. Our method generalizes Stochastic Forward-Backward Deconvolution (SFBD; Lu et al., 2025) to handle arbitrary measurement models beyond Gaussian corruption. Experiments across benchmark datasets and diverse measurement settings demonstrate significant improvements in both qualitative and quantitative performance.
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