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Peak Persistence Diagrams for Shape-Based Signal Estimation
Woo Min Kim1, Sutanoy Dasgupta2, Pavan Turaga3
1Department of Statistics, Florida State University, Tallahassee, FL 32306, USA.
IEEE Transactions on Signal Processing : a Publication of the IEEE Signal Processing Society
|January 16, 2026
Summary
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.
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.
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