Raman spectroscopy can be used to identify molecules such as DNA by the characteristic scattering of light from a laser. It is sensitive at very low concentrations and can accurately quantify the amount of a given molecule in a sample. The presence of a large, nonuniform background presents a major challenge to analysis of these spectra. To overcome this challenge, we introduce a sequential Monte Carlo (SMC) algorithm to separate the observed spectrum into a series of peaks plus a smoothly-varying baseline, corrupted by additive white noise. The peaks are modelled using Lorentzian or Gaussian broadening functions, while the baseline is estimated using a penalised cubic spline. This latent continuous representation accounts for differences in resolution between measurements. By incorporating this representation in a Bayesian model, we can quantify the relationship between molecular concentration and peak intensity, thereby providing an improved estimate of the limit of detection (LOD), which is of major importance in analytical chemistry.

翻译：拉曼光谱可通过激光照射下物质对光的特征散射来识别DNA等分子。该方法在极低浓度下仍具有高灵敏度，并能精确量化样品中特定分子的含量。然而，光谱中存在显著且不均匀的背景信号，这对光谱分析构成了主要挑战。为应对这一挑战，我们引入了一种序贯蒙特卡洛（SMC）算法，将观测光谱分解为一系列谱峰与平滑变化的基线之和，并叠加加性白噪声。谱峰采用洛伦兹或高斯展宽函数建模，基线则通过惩罚三次样条进行估计。这种潜在的连续表示能够解释不同测量间分辨率的差异。通过将该表示纳入贝叶斯模型，我们能够量化分子浓度与谱峰强度之间的关系，从而提供更准确的检测限（LOD）估计值，这在分析化学领域具有重要意义。