Matching Pursuit for Denoising Raman Spectra, Based on Genetic Algorithm and Hermite Atoms

Due to its various advantages, Raman spectroscopy has become a powerful tool in different fields of science and engineering; however, in specific applications, this technique's limiting factor is closely related to the inherent noise of the Raman spectra. To eliminate the noise of a Raman spectrum, preserving its position, intensity, and width characteristic, we propose using a genetic matching pursuit-Hermite atoms (GMP-HAs) algorithm in this work. This algorithm helps recover Raman spectra immersed in Gaussian noise with the least number of atoms. The noise-free Raman signal is reconstructed with the GMP-HAs algorithm, transforming the typical best-matching atom search into an optimization problem. Specifically, we maximize the fitness function, defined as the correlation between current residual and Hermite atoms, with the genetic algorithm MI-LXPM encoded in a real domain and avoiding local maxima, by adding a stopping criterion based on an exponential adjustment according to the algorithm's behavior in the presence of noise. Simulated and biological Raman spectra are used to evaluate the proposed algorithm and compare its performance with typically known methods for denoising, such as the Savitzky- Golay filter (SG) and basis pursuit denoising. Using the signal-to-noise ratio (S/N)metric resulted in a 0.31 dB advantage in the S/N product for the proposed algorithm with respect to SG. Additionally, it is shown that the algorithm uses only 25.3% of the number of atoms needed by the matching pursuit algorithm. The results indicate that the GMP-HAs algorithm has better denoising capabilities, and at the same time, the Raman spectra are decomposed with fewer atoms compared to known sparse algorithms.