Adaptive Iterative Reweighted Penalized Least Squares Method for Background Subtraction in Raman Spectroscopy or Chromatographic Data

In the analysis of Raman spectroscopy or chromatographic data, background subtraction plays a critical role in data preprocessing. To achieve this objective, we can implement the Adaptive Iterative Reweighted Penalized Least Squares (airPLS) method. This algorithm employs a weighted least squares approach with adaptive iteration to effectively remove baseline drift and noise interference while preserving meaningful spectral features. The core implementation involves iteratively adjusting weights based on residual values between the original signal and fitted baseline, with a penalty term controlling the smoothness of the baseline estimation. Key computational steps include: 1. Initializing weights uniformly and setting convergence tolerance 2. Solving penalized least squares problem with diagonal weight matrix 3. Updating weights based on negative residuals using asymmetric weighting function 4. Iterating until the sum of negative residuals meets convergence criteria This method demonstrates particular effectiveness in handling complex backgrounds through its adaptive reweighting mechanism, which automatically assigns lower weights to potential peak regions during baseline fitting. The algorithm provides superior accuracy and reliability in background correction compared to traditional polynomial fitting methods. For practical implementation, the method requires tuning parameters such as smoothness factor (lambda) and convergence threshold, which can be optimized through cross-validation for specific instrumentation characteristics. We strongly recommend adopting this approach for Raman spectroscopy or chromatographic data analysis to obtain cleaner spectral signatures and improved quantitative results.