Detecting Non-Overlapping Signals with Dynamic Programming

Area of Science:

• Signal Processing
• Optimization Algorithms
• Computational Statistics

Background:

• Accurate detection of signal occurrences in noisy environments is a fundamental challenge.
• Existing methods may struggle with dense signal occurrences or model uncertainties.

Purpose of the Study:

• To develop a computationally efficient and robust algorithm for detecting signal locations in one-dimensional noisy measurements.
• To address the classical problem of non-overlapping signal detection.

Main Methods:

• Formulation of signal detection as a constrained likelihood optimization problem.
• Design of a dynamic programming algorithm to find the optimal solution.
• Evaluation through extensive numerical experiments.

Main Results:

• The proposed dynamic programming algorithm accurately estimates signal locations in dense and noisy conditions.
• The framework demonstrates scalability and robustness to model uncertainties.
• The algorithm outperforms existing alternative methods in numerical tests.

Conclusions:

• The developed dynamic programming approach offers an effective solution for signal detection problems.
• The method is suitable for practical applications requiring accurate and efficient signal localization.
• The algorithm's robustness and accuracy make it a valuable tool in signal processing.