标题： 使用归一化流避免随机信号的减法和除法：NFdeconvolve 显示英文标题

标题： Avoiding subtraction and division of stochastic signals using normalizing flows: NFdeconvolve

摘要： 在科学领域，我们会遇到减去或除以随机信号的情况。例如，考虑一个随机实现 $x$，它由两个随机信号 $a$ 和 $b$ 的相加或相乘生成，即 $x=a+b$ 或 $x = ab$。 对于$x=a+b$示例，$a$可以是荧光背景，而$b$是感兴趣的信号，其统计特性需要从测量的$x$中学习。类似地，在书写$x=ab$时，$a$可以看作是激发光强度，而$b$是感兴趣荧光分子的密度。 然而，对随机信号进行除法或减法会放大噪声，我们转而询问，是否可以利用 $a$的统计信息和 $x$的测量值作为输入，来恢复 $b$的统计信息。 在这里，我们展示了如何使用归一化流生成 $b$上概率分布的近似值，从而完全避免了减法或除法。 该方法已在我们的软件包 NFdeconvolve 中实现，该软件包可在 GitHub 上获取，并且主文本中附有相关教程链接。 显示英文摘要

摘要： 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.