Coding Prony's method in MATLAB and applying it to biomedical signal filtering

Area of Science:

• Biomedical Signal Processing
• Computational Mathematics
• Medical Diagnostics

Background:

• Biomedical system responses are often modeled using damped exponential functions.
• Prony's method and its variants are used for parameter approximation from sampled data.
• This study focuses on polynomial Prony and matrix pencil methods for signal analysis.

Purpose of the Study:

• To provide a tutorial on polynomial Prony and matrix pencil methods.
• To implement and test these methods in MATLAB for synthetic and multifocal visual-evoked potential (mfVEP) signals.
• To evaluate their performance in improving multiple sclerosis (MS) diagnosis through mfVEP filtering.

Main Methods:

• Theoretical basis of four polynomial Prony methods: classic, least squares (LS), total least squares (TLS), and matrix pencil method (MPM).
• Implementation using general MATLAB functions.
• Testing with synthetic functions and mfVEP signals for approximation and filtering.

Main Results:

• LS and MPM methods demonstrated the best performance in signal approximation among those tested.
• Filtering mfVEP signals in the Prony domain yielded an area under the ROC curve of 0.7055.
• This improved diagnostic performance compared to the standard discrete Fourier transform low-pass filter (0.6538).

Conclusions:

• Prony's method is valuable for biomedical signal filtering and approximation.
• MATLAB code for classic, LS, TLS, and MPM methods is provided.
• Enhancing computational methods for these techniques is crucial for improved biomedical applications.