Baseline Algorithms

OpticalSpectroscopy.jl provides baseline correction algorithms that take different approaches and perform best in different situations. This page explains the tradeoffs to help you choose.

The Baseline Problem

Spectroscopic signals sit on top of a slowly varying background caused by fluorescence, scattering, detector drift, or optical effects. Baseline correction estimates and removes this background so that peak parameters (position, width, area) can be measured accurately.

A good baseline algorithm should:

• Follow the slowly varying background
• Not be pulled upward by peaks
• Require minimal manual tuning

Algorithm Summary

ALS (the classic asymmetric least squares method) is not exported as its own function; arPLS supersedes it for practical work. The ALS algorithm is discussed below for context.

arPLS (Asymmetrically Reweighted Penalized Least Squares)

baseline = arpls_baseline(y; λ=1e5)

arPLS is the recommended default. It improves on ALS by automatically determining the asymmetry weights from the statistics of negative residuals (points below the current baseline estimate). This eliminates the need to tune the p parameter.

How it works: At each iteration, points far above the baseline get low weight (they're peaks), while points near or below the baseline get high weight (they're background). The weighting uses a sigmoid function centered at $-\mu + 2\sigma$ of the negative residuals, where $\mu$ and $\sigma$ are the mean and standard deviation.

When to use: Start here. Works well for FTIR, Raman, UV-vis, and most spectroscopy data.

Tuning $\lambda$:

• Higher $\lambda$ = smoother baseline (ignores local variations)
• Lower $\lambda$ = baseline follows local structure more closely
• Typical range: $10^4$ to $10^8$
• If baseline cuts through peaks: increase $\lambda$
• If baseline doesn't follow broad curvature: decrease $\lambda$

Reference: Baek et al. (2015). Analyst, 140(1), 250-257.

ALS (Asymmetric Least Squares)

ALS is the conceptual predecessor to arPLS. OpticalSpectroscopy.jl does not export a standalone als_baseline function — arpls_baseline is recommended instead and supersedes plain ALS for almost all practical work. The weighted-update idea that ALS introduced is what arPLS extends with automatic reweighting.

ALS uses a fixed asymmetry parameter p to weight residuals. Points above the baseline are weighted by p (small), points below by 1-p (large). This pushes the baseline below peaks.

How it works: Minimizes a penalized objective:

\[\sum_i w_i (y_i - z_i)^2 + \lambda \sum_i (\Delta^2 z_i)^2\]

The first term fits the data (with asymmetric weights), and the second term penalizes roughness (second differences of the baseline).

Tuning (conceptual):

• $\lambda$: smoothness (same as arPLS)
• $p$: asymmetry (0.001 to 0.05). Lower values keep the baseline further below peaks. If peaks are being clipped, decrease p.

The main drawback — needing to hand-tune p — is exactly what arPLS removes by deriving the weighting from residual statistics.

Reference: Eilers & Boelens (2005). Leiden University Medical Centre Report.

SNIP (Statistics-sensitive Non-linear Iterative Peak-clipping)

baseline = snip_baseline(y; iterations=40)

SNIP takes a fundamentally different approach: instead of fitting a smooth function, it iteratively clips peaks by replacing each point with the minimum of itself and the average of its neighbors at increasing distances.

How it works: For each iteration with window size $k$:

\[z_i = \min(z_i, (z_{i-k} + z_{i+k}) / 2)\]

By default, window sizes decrease from iterations down to 1. This handles broad features first, then refines around narrow peaks.

When to use: Spectra with many overlapping peaks where penalized methods struggle to find the true baseline. Common in Raman spectroscopy of complex materials, XRD patterns, and energy-dispersive X-ray spectra.

Tuning iterations: Should be roughly half the width (in data points) of the widest peak. More iterations produce a smoother baseline. For a 2048-point Raman spectrum with peaks ~80 points wide, try iterations=40.

Advantages over PLS methods:

• No smoothness parameter to tune
• Handles many overlapping peaks naturally
• Computationally simpler

Disadvantages:

• Less smooth baseline (can show small artifacts)
• May not follow gradual curvature as well

Reference: Ryan et al. (1988). Nuclear Instruments and Methods B, 34(3), 396-402.

Choosing an Algorithm

Is this a routine analysis with isolated or moderately overlapping peaks?
  → Use arPLS (default)

Does arPLS cut through peaks or miss broad curvature?
  → Try adjusting λ first

Does the spectrum have many heavily overlapping peaks?
  → Use SNIP

Practical Tips

1. Always plot the baseline overlaid on the raw spectrum before trusting the correction. All baseline functions return just the baseline vector, so you can inspect it:

   baseline = arpls_baseline(y)
   lines(x, y)
   lines!(x, baseline, color=:red)

2. Use correct_baseline for convenience — it returns both the corrected spectrum and the baseline in a named tuple:

   result = correct_baseline(x, y; method=:arpls)
   result.y        # corrected
   result.baseline  # the baseline

3. Baseline correction before peak fitting can improve results, but fit_peaks already includes a polynomial baseline in the fit model. For well-isolated peaks, the built-in baseline may be sufficient.

4. Baseline correction for peak detection is available directly in find_peaks:

   peaks = find_peaks(x, y; baseline=:arpls)

References

1. Eilers, P. H. C., & Boelens, H. F. M. (2005). Baseline Correction with Asymmetric Least Squares Smoothing.
2. Baek, S.-J., Park, A., Ahn, Y.-J., & Choo, J. (2015). Baseline correction using asymmetrically reweighted penalized least squares smoothing. Analyst, 140(1), 250-257.
3. Ryan, C. G., et al. (1988). SNIP, a statistics-sensitive background treatment. Nuclear Instruments and Methods B, 34(3), 396-402.
4. Morháč, M., & Matoušek, V. (2008). Peak Clipping Algorithms for Background Estimation. Applied Spectroscopy, 62(1), 91-106.