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Peak Persistence Diagrams for Shape-Based Signal Estimation.

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  • 1Department of Statistics, Florida State University, Tallahassee, FL 32306, USA.

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|January 16, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a novel signal estimation method using topological and geometric data features. The penalized elastic signal alignment (PESA) approach improves accuracy for signals with additive and warping noise.

Keywords:
dynamic time warpingelastic alignmentpeak persistenceshape estimationshape-constrained signalsignal estimation

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Area of Science:

  • Signal Processing
  • Data Analysis
  • Computational Topology

Background:

  • Signal estimation from noisy data is a core challenge.
  • Existing methods rely on specific model choices and criteria.
  • A need exists for robust estimators handling complex noise types.

Purpose of the Study:

  • To develop an innovative signal estimation framework using topological and geometric data features.
  • To introduce a peak-persistence diagram (PPD) for signal shape analysis.
  • To provide a robust estimator for signals with both additive and warping noise.

Main Methods:

  • Leveraging the penalized elastic signal alignment (PESA) framework.
  • Utilizing peak-persistence diagrams (PPD) to estimate signal shape (peaks/valleys).
  • Employing shape-constrained optimization for signal estimation.

Main Results:

  • The PESA approach balances signal averaging and elastic alignment.
  • A computationally efficient procedure for the proposed method is presented.
  • Demonstrated superior performance against state-of-the-art techniques in simulations and real-world data.

Conclusions:

  • The proposed PESA framework offers a significant advancement in signal estimation.
  • Effective for analyzing complex datasets like COVID rate and electricity consumption curves.
  • Highlights the utility of topological features in signal processing.