Global fitting without a global model: regularization based on the continuity of the evolution of parameter...

Area of Science:

• Spectroscopy
• Data Analysis
• Computational Chemistry

Background:

• Global data fitting is crucial for analyzing complex spectroscopic datasets.
• Traditional methods often rely on specific models, limiting flexibility.
• Physically realistic constraints can stabilize data fitting procedures.

Purpose of the Study:

• To introduce a new global data fitting approach using continuity regularization.
• To enhance the analysis of spectroscopic data, including dynamic light scattering and time-correlated single-photon counting (TCSPC).
• To demonstrate the method's ability to recover subtle data features compared to traditional techniques.

Main Methods:

• A novel regularization condition based on continuity in the global data coordinate.
• Probabilistic constraint of the global solution to physically reasonable behavior.
• Application to various spectroscopic data types and comparison with inverse Laplace transform fitting.

Main Results:

• The new method stabilizes the data fitting procedure.
• It successfully recovers features in synthetic TCSPC data not apparent with traditional fitting.
• The approach allows a transition from model-free to model-specific fitting.

Conclusions:

• The proposed global data fitting method offers a robust alternative for spectroscopic data analysis.
• It provides superior feature recovery and flexibility compared to conventional methods.
• This technique facilitates a progressive approach from model-free to deterministic data fitting.