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Wavelet invariants for statistically robust multi-reference alignment.

Matthew Hirn1, Anna Little2

  • 1Department of Computational Mathematics, Science and Engineering, Department of Mathematics and Center for Quantum Computing, Science and Engineering, Michigan State University, East Lansing, MI 48824.

Information and Inference : a Journal of the IMA
|January 24, 2022
PubMed
Summary
This summary is machine-generated.

We developed a novel wavelet-based signal method that is resilient to noise and distortions. This technique accurately reconstructs signal power spectra, overcoming limitations of traditional methods.

Keywords:
method of invariantsmulti-reference alignmentsignal processingwavelet scattering transformwavelets

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Area of Science:

  • Signal processing
  • Wavelet analysis
  • Statistical signal processing

Background:

  • Traditional signal representations often struggle with noise and distortions.
  • Multi-reference alignment problems require robust signal analysis techniques.
  • Power spectrum estimation is crucial for many signal processing applications.

Purpose of the Study:

  • To introduce a nonlinear, wavelet-based signal representation.
  • To demonstrate translation invariance and robustness to noise and dilations.
  • To develop a method for accurate power spectrum recovery from corrupted signals.

Main Methods:

  • Utilizing a nonlinear, wavelet-based signal representation.
  • Analyzing statistical properties with numerous signal corruptions.
  • Applying an unbiasing procedure to remove noise and dilation effects.
  • Solving a convex optimization problem for power spectrum approximation.
  • Reducing the problem to a phase retrieval task.

Main Results:

  • The proposed representation uniquely defines the power spectrum.
  • An effective unbiasing procedure was developed for the representation.
  • Accurate power spectrum approximation was achieved via convex optimization.
  • Extensive experiments confirmed the statistical robustness of the procedure.

Conclusions:

  • The nonlinear wavelet-based representation offers a robust alternative for signal analysis.
  • This method enables accurate power spectrum recovery even with significant noise and distortions.
  • The approach provides a novel solution to phase retrieval problems in signal processing.