Bandwidth Detection of Graph Signals with a Small Sample Size

Area of Science:

• Signal Processing
• Graph Signal Processing
• Statistical Inference

Background:

• Bandwidth is critical for graph signal (GS) processing tasks like sampling and reconstruction, but it's often unknown in practical scenarios.
• Existing methods struggle with high-dimensional challenges where the number of spectral components exceeds the available sample size.

Discussion:

• This paper proposes a novel multi-stage Bayesian score test for detecting the bandwidth of bandlimited graph signals.
• The method addresses the challenge of a small sample size relative to the number of spectral components.
• Each stage employs a Bayesian score test with priors on spectral components to manage high dimensionality.

Key Insights:

• The Bayesian score test is designed to be locally most powerful in expectation against alternatives matching the prior.
• Different priors are utilized in each stage to enhance test power against similar bandwidth alternatives.
• Numerical analysis confirms the method's effectiveness and robustness to noise in bandwidth detection.

Outlook:

• This approach offers a robust solution for bandwidth estimation in graph signal processing.
• Future work could explore adaptive prior selection for further performance gains.
• The method has potential applications in various fields relying on graph signal analysis.