关键词: 小波变换, 信号去噪, 深度学习, 高效液相色谱

Abstract: High performance liquid chromatography (HPLC) signals are often contaminated by random noise during acquisition and transmission. Thermal noise, electrical noise, and instrumental drift are major disturbance sources. These disturbances increase baseline fluctuation and distort chromatographic peak profiles. They also reduce the reliability of peak detection and quantitative analysis. Therefore, robust chromatographic signal denoising remains an important preprocessing step.
In this study, a denoising algorithm based on a wavelet-domain multi-scale convolutional neural network (MSCNN) is proposed. The method is designed for one-dimensional HPLC signals. It combines wavelet decomposition with deep feature learning. The main objective is to improve noise suppression while preserving peak shape fidelity. The method is also intended for a broad input signal-to-noise ratio (SNR) range.
The noisy signal is first processed by a four-level discrete wavelet transform (DWT). This operation generates one approximation coefficient set and four detail coefficient sets. Instead of denoising the raw signal directly, the proposed model learns a mapping in the wavelet domain. Five scale-specific encoders are constructed for the five wavelet subbands. These encoders do not share parameters. Each encoder extracts features from one specific scale. This design helps the model distinguish broad peaks from fine-scale noise. After scale-wise encoding, a multi-scale fusion module is used to aggregate information across all scales. The fused features are then sent to five output heads. Each output head reconstructs one denoised coefficient sequence. The final denoised chromatographic signal is obtained by inverse wavelet reconstruction.
A simulated HPLC dataset was constructed for training and evaluation. The dataset contains 500 chromatographic signals. Each signal contains 8 000 sampling points over 0‒20 min. The input SNR covered a range of 1‒35 dB. The dataset was divided into training, validation, and test subsets. The split ratio was 6:2:2. The model was trained with the L1 loss function. The AdamW optimizer was used during training.
Wavelet basis selection was also investigated. Symlets wavelets from sym2 to sym11 were compared. All wavelets were tested under the same network configuration. The results showed that sym11 achieved the best overall performance balance. It provided the highest denoising performance with good peak preservation. Therefore, sym11 was selected as the fixed wavelet basis in the final model.
Denoising performance was evaluated by SNR improvement and root mean square error (RMSE). On the original test set, MSCNN achieved an average SNR improvement of 23.84 dB. The average RMSE was 0.021. In the low-SNR region below 10 dB, the average SNR improvement reached 25.38 dB. These results indicate strong robustness to severe noise conditions They also demonstrate accurate signal reconstruction after denoising.
An additional overlap-peak experiment was further designed. This experiment examined signal fidelity under complex peak-shape conditions. Test samples were reorganized as overlapped double-peak chromatograms. The input SNR was fixed at 5 dB. Different overlap levels were controlled by chromatographic resolution. Five representative resolution levels were used. The average RMSE was then calculated for all algorithms. The overlap-peak results were consistent with the main experiment. The RMSE of all methods decreased as resolution increased. This trend indicated lower reconstruction difficulty at better peak separation. More importantly, MSCNN maintained the lowest RMSE at all tested resolution levels. This result demonstrated strong fidelity in overlapped peak scenarios. It also showed that the proposed method was not only effective on ordinary synthetic signals but also remained accurate when peak overlap became prominent.
A real chromatographic dataset acquired from an Agilent 1260 Infinity Ⅱ system was also used for validation. The denoised signal showed much weaker high-frequency baseline fluctuation. Noise around peak shoulders was also strongly suppressed. Meanwhile, the main peak position remained stable. Peak width and local peak profile were also well preserved. No obvious pseudo-peaks were introduced. No clear oversmoothing was observed.
In summary, this study develops an effective HPLC signal denoising method by combining wavelet-domain representation with multi-scale deep feature learning. The proposed MSCNN achieves high SNR improvement and low RMSE. It also preserves peak shape over a broad SNR range. The additional overlap-peak experiment further confirms its robustness. Real sample validation also supports its practical value. Therefore, the proposed method provides a useful tool for chromatographic preprocessing, weak-peak extraction, and high-precision quantitative analysis.

Key words: wavelet transform, signal denoising, deep learning, high performance liquid chromatography