Compressive Detection of Highly Overlapped Spectra Using Walsh-Hadamard-Based Filter Functions.

Area of Science:

• Chemometrics
• Spectroscopy
• Data Science

Background:

• Spectral analysis often involves large datasets, necessitating efficient data reduction strategies.
• Compressive sensing offers a paradigm for acquiring signals below the Nyquist rate.
• Walsh functions provide a suitable orthonormal basis for binary signal processing.

Purpose of the Study:

• To develop and validate a compressive detection strategy for rapid analyte score determination in mixtures.
• To construct optimized spectral filter functions using Walsh functions and genetic algorithm principles.
• To demonstrate the method's ability to handle highly overlapped spectral data and remove baseline artifacts.

Main Methods:

• Construction of spectral filter functions based on binary fourfold linear combinations of Walsh functions.
• Optimization of filter functions using genetic algorithm-inspired mathematics for specific analyte sets.
• Application of filter functions within a spectrometer for on-the-fly score determination.
• Monte Carlo simulations with Raman and excitation-emission matrix (EEM) data.

Main Results:

• Successful determination of analyte scores from mixtures with highly overlapped spectral loadings.
• Significant data set shrinkage achieved through compressive detection.
• Effective automatic baseline stripping integrated into the filter functions.
• Robust estimation of true scores even with noisy data, confirming method linearity.

Conclusions:

• The developed method enables efficient, on-the-fly determination of analyte scores in complex mixtures using compressive detection.
• Walsh functions and genetic algorithm optimization provide a powerful framework for designing effective spectral filter functions.
• This approach offers a significant advancement in spectral data analysis, particularly for highly overlapped spectra.