通过相位可靠性加权，实现噪声环境下视频运动放大的精准控制。
Fractional-Order Adaptive Motion Magnification: Phase-Reliability Weighting for Noise-Constrained Video Amplification
- 用分数阶导数动态调节高频增强，替代固定增益。
- 在纹理缺失区域保持噪声与输入水平一致，降噪效果提升八倍信噪比范围。
- 适合需要高精度运动放大且对背景噪声敏感的应用场景。
欧拉法视频放大通过带通滤波像素强度变化并施加统一增益来增强亚像素运动，但该增益忽略局部结构，导致传感器噪声与信号一同被放大，尤其在无纹理区域因单色相位不可靠而加剧。本文提出FrAM（分数阶自适应运动放大），先离线后以因果流形式处理。将恒定时间增益替换为格伦瓦尔德-莱特尼科夫分数阶导数，实现对高频强调的连续控制；将均匀空间增益替换为基于局部单色信号幅度的逐像素权重。在合成数据中，纹理与平坦区域分离测试显示，FrAM 在匹配欧拉基线放大效果的同时，使平坦区域的时间噪声维持在输入水平，且该优势在八倍输入噪声范围内持续有效。真实视频实验表明，所有案例均表现出更优的空间选择性与更低的背景噪声。因果重构将每帧计算成本降低两个数量级，640×480分辨率下达到69帧/秒。
原文摘要 · Abstract (English)
Eulerian video amplification boosts sub-pixel motion by band-pass filtering per-pixel intensity traces and applying a uniform gain. That gain ignores local structure, so sensor noise is amplified together with the signal, especially in textureless regions where the monogenic phase is unreliable. We propose FrAM (Fractional-order Adaptive Motion Magnification), a pipeline developed first offline and then as a causal stream. It replaces the constant temporal gain with a Gr\"unwald--Letnikov derivative of fractional order, giving continuous control over high-frequency emphasis, and replaces the uniform spatial gain with a per-pixel weight derived from the local amplitude of the monogenic signal. On a controlled synthetic sequence split into textured and flat halves, FrAM matches the amplification of the Eulerian baseline while keeping flat-region temporal noise at the input level. The reduction holds across an eightfold range of input noise levels. Real videos show improved spatial selectivity and lower background noise in every case. The causal reformulation cuts the per-frame cost by two orders of magnitude, reaching 69\,fps at 640$\times$480.
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