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

2025-01-14

AI Summary

Traditional subtraction/division-based inversion methods for random signals corrupted by combined additive and multiplicative noise suffer from noise amplification and numerical instability. To address this, we propose an end-to-end probabilistic inversion framework based on normalizing flows (NFs). This work is the first to employ invertible neural networks—structured as normalizing flows—to directly model the posterior distribution of latent components, thereby circumventing explicit decoupling operations and enabling statistically robust learning of latent variable distributions. The method integrates maximum likelihood estimation with exact probability density transformation and is implemented in the open-source toolkit NFdeconvolve. Experiments demonstrate substantial improvements in fluorescence background suppression and molecular density estimation: signal-to-noise ratio increases by +8.2 dB, and KL divergence—measuring statistical fidelity—decreases by 37%. Our approach establishes a new paradigm for probabilistic inversion of stochastic signals.

Technology Category

Machine Learning: Probabilistic Circuits and Graphical ModelsReasoning under Uncertainty: Probabilistic InferenceIntelligent Robots: State Estimation

Application Category

Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSecurity and Privacy: Data transparency and provenance

Abstract

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.

Problem

• Signal Processing
• Random Noise
• Accuracy Degradation

Innovation

• Normalized Flows
• Noise-resistant Signal Processing
• Direct Signal Characterization