This is a problem we are also currently working on (added two recently published papers below), because we found it unresolved yet, and high-throughput experiments nowadays require more automated high-throughput analyses.
A first set of causes are DSP-like disturbances on the "interesting peak data": non-linearity (like saturation), added noise (with unknown distributions) and baselines (with unknown regularity). They can related to solute or matrix effects, type of chromatography (liquid, gas), columns, detectors, the complexity of the mixture, etc. We can include more or less visible processing performed inside the measurement tools: sampling (how any points per peaks?), smoothing, normalizations.
In gas chromatography there are models like Gaussian shapes, that can be explained by physical models (plates). However, separated peaks can exhibit distorsions such as fronting and tailing, or other asymmetries, that can vary throughout the chromatogram in uneven manners.
Even with "nicely"-sampled discrete Gaussians, very close peaks may be difficult to separate or distinguish (shouldering effects). More globally, deconvolution of sums of Gaussians remains difficult, because the direct problem is ill-posed: there are many ways to fit a single Gaussian with one of several Gaussians, and algorithms require additional optimization terms (constraints, regularization), that come with tuning parameters when combined with the data fidelity term (often a least-squares, but other choices are interesting).
As far as I know, such issues exists in other analytical chemistry modalities: NMR, infrared, mass spectrometry, Raman etc., each with their own issues. Variable peak shifting related to molecule interactions in NMR is a challenge for subsequent (blind) source separation algorithms.
There are works on using more machine learning techniques, yet it is likely that using physical or DSP models would help them.
A possible starting point on the difficulties of fitting: Dependence of Chromatogram Peak Areas Obtained by Curve-Fitting on the Choice of Peak Shape Function, 1997
We recently considered a couple of methods towards reconstruction or recovery of physico-chemical signals. They definitely are not the end of the game:
SPOQ ℓp-Over-ℓq Regularization for Sparse Signal Recovery applied to Mass Spectrometry, IEEE Transactions on Signal Processing, 2020 (Matlab code SPOQ toolbox)
Underdetermined or ill-posed inverse problems require additional
information for \ldd{d} sound solutions with tractable optimization
algorithms. Sparsity yields consequent heuristics to that matter, with
numerous applications in signal restoration, image recovery, or
machine learning. Since the ℓ0 count measure is barely tractable, many
statistical or learning approaches have invested in computable
proxies, such as the ℓ1 norm. However, the latter does not exhibit the
desirable property of scale invariance for sparse data. Extending the
SOOT Euclidean/Taxicab ℓ1-over-ℓ2 norm-ratio initially introduced for
blind deconvolution, we propose SPOQ, a family of smoothed
(approximately) scale-invariant penalty functions. It consists of a
Lipschitz-differentiable surrogate for ℓp-over-ℓq quasi-norm/norm
ratios with p∈]0,2[ and q≥2. This surrogate is embedded into a novel
majorize-minimize trust-region approach, generalizing the variable
metric forward-backward algorithm. For naturally sparse
mass-spectrometry signals, we show that SPOQ significantly outperforms
ℓ0, ℓ1, Cauchy, Welsch, SCAD and Celo penalties on several performance
measures. Guidelines on SPOQ hyperparameters tuning are also provided,
suggesting simple data-driven choices.
Sparse Signal Reconstruction for Nonlinear Models via Piecewise Rational Optimization, Signal Processing, 2021
We propose a method to reconstruct sparse signals degraded by a
nonlinear distortion and acquired at a limited sampling rate. Our
method formulates the reconstruction problem as a nonconvex
minimization of the sum of a data fitting term and a penalization
term. In contrast with most previous works which settle for
approximated local solutions, we seek for a global solution to the
obtained challenging nonconvex problem. Our global approach relies on
the so-called Lasserre relaxation of polynomial optimization. We here
specifically include in our approach the case of piecewise rational
functions, which makes it possible to address a wide class of
nonconvex exact and continuous relaxations of the ℓ0 penalization
function. Additionally, we study the complexity of the optimization
problem. It is shown how to use the structure of the problem to
lighten the computational burden efficiently. Finally, numerical
simulations illustrate the benefits of our method in terms of both
global optimality and signal reconstruction.
