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

Pedro Pessoa1,2, Max Schweiger1,2, Lance W Q Xu1,2

  • 1Center for Biological Physics, Arizona State University, Tempe, AZ, USA.

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This study introduces normalizing flows to recover underlying stochastic signals from combined measurements, avoiding noise amplification from subtraction or division. The NFdeconvolve software package implements this novel approach for signal recovery.

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Area of Science:

  • Signal processing
  • Statistical inference
  • Computational science

Background:

  • Stochastic signals are common in science, often combined through addition or multiplication.
  • Directly isolating one signal (e.g., fluorescence background) from a combined measurement (e.g., total fluorescence) is challenging.
  • Traditional methods like subtraction or division amplify noise, hindering accurate statistical learning.

Purpose of the Study:

  • To develop a method for recovering the statistics of a component stochastic signal (b) from a combined signal (x) and known statistics of another component (a).
  • To avoid the noise amplification issues inherent in direct subtraction or division operations.
  • To provide a practical software implementation for this novel signal recovery technique.

Main Methods:

  • Utilizing normalizing flows, a class of deep generative models, to approximate probability distributions.
  • Applying normalizing flows to model the distribution of the unobserved signal 'b' given the observed signal 'x' and the statistics of signal 'a'.
  • Developing the NFdeconvolve software package to implement the normalizing flow-based deconvolution.

Main Results:

  • Demonstrated that normalizing flows can effectively approximate the probability distribution of the target signal 'b'.
  • Showcased the ability to recover signal statistics without resorting to direct subtraction or division.
  • Successfully implemented the method in the NFdeconvolve software, making it accessible to researchers.

Conclusions:

  • Normalizing flows offer a powerful alternative to traditional methods for deconvolving stochastic signals.
  • This approach mitigates noise amplification, leading to more robust statistical inference.
  • The NFdeconvolve package provides a valuable tool for scientific research involving complex stochastic signal analysis.