用归一化流直接推断信号分布，避免噪声放大的减除操作。
Avoiding subtraction and division of stochastic signals using normalizing flows: NFdeconvolve
- 基于归一化流构建信号统计推断模型
- 从观测信号中恢复目标信号的分布，无需直接除法或减法
- 适用于荧光成像等噪声敏感场景，代码开源可复现
在科学计算中，常需对随机信号进行减法或除法操作。例如，当观测信号 x = a + b 时，a 可能是荧光背景，b 是感兴趣的信号；若 x = ab，a 为光照强度，b 为荧光分子密度。直接减除或除法会放大噪声。本文提出利用归一化流（normalizing flows）方法，仅根据信号 a 的统计特性与观测值 x，重建目标信号 b 的概率分布，从而避免直接运算。该方法已实现于开源软件 NFdeconvolve，附带教程，便于在实际应用中部署。
原文摘要 · Abstract (English)
Across the scientific realm, we find ourselves subtracting or dividing stochastic signals. For instance, consider a stochastic realization, $x$, generated from the addition or multiplication of two stochastic signals $a$ and $b$, namely $x=a+b$ or $x = ab$. For the $x=a+b$ example, $a$ can be fluorescence background and $b$ the signal of interest whose statistics are to be learned from the measured $x$. Similarly, when writing $x=ab$, $a$ can be thought of as the illumination intensity and $b$ the density of fluorescent molecules of interest. Yet dividing or subtracting stochastic signals amplifies noise, and we ask instead whether, using the statistics of $a$ and the measurement of $x$ as input, we can recover the statistics of $b$. Here, we show how normalizing flows can generate an approximation of the probability distribution over $b$, thereby avoiding subtraction or division altogether. This method is implemented in our software package, NFdeconvolve, available on GitHub with a tutorial linked in the main text.
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