Deep Residual Neural Networks For Robust Denoising In Raman Spectroscopy

Abstract

Raman spectroscopy is a key tool for material analysis, but its accuracy is often hindered by noise and baseline distortions. This paper presents a robust denoising method using a parallel deep residual neural network architecture based on DnCNN, designed for one-dimensional spectral data. The model learns noise patterns through multiple convolutional branches, enabling efective denoising without assumptions about the signal origin. We evaluate several pre-processing techniques, with minimum-shift normalization proving most efective in preserving spectral features. Trained on datasets with varying noise levels, the network achieves high peak detection accuracy and low error rates, outperforming traditional and recent methods. This approach enhances the reliability of Raman analysis and demonstrates the potential of AI-driven models in spectroscopy and time-series signal processing.

Keywords

• eol>Residual Learning Neural Network
• One-Dimensional Signal Denoising
• Raman Spectrum
• Time-Series Signal

1. Introduction

material characterization. However, Raman signals often sufer from noise that obscures peaks and non-uniform Denoising methods are fundamental across numerous baselines, complicating interpretation. Among the variscientific disciplines. Their purpose is to eliminate noise ous types of signal corruption [1], baseline distortion and introduced during the acquisition of a signal, image, high peak noise are the most problematic [2], as the analor other data. In this project, the focus is on one- ysis heavily relies on peak characteristics [3]. These peak dimensional signals obtained from Raman spectroscopy, characteristics, such as position, intensity, width, and a non-destructive material analysis technique based on shape, are used to identify substances and measure their the scattering of monochromatic electromagnetic radia- concentrations. When noise is too strong, even expert tion by a sample. analysts may misinterpret spectra, leading to incorrect

Raman spectroscopy is crucial for studying materials conclusions. in solid, liquid, or gaseous states, particularly carbon- To address these issues, the scientific community has based materials such as graphite and graphene. It also developed numerous denoising techniques. Traditional ifnds applications in geological research, industrial pro- signal processing methods such as Empirical Mode Decess control, planetary exploration, internal security, and composition (EMD) [ 4 ] and wavelet analysis have been even medical diagnostics when combined with artificial widely applied. EMD is attractive because it does not intelligence to analyze cancer cells and melanomas. require any prior knowledge of the signal or noise struc

The key strength of Raman spectroscopy lies in its abil- ture, but it is often unstable and sensitive to noise itself. ity to detect subtle molecular vibrations that are specific Wavelet transforms, on the other hand, allow localized to the chemical bonds within the sample. This makes analysis in both time and frequency domains, but they it extremely valuable for both qualitative and quanti- require careful selection of wavelet families and threshtative analyses. However, the full potential of Raman olds. spectroscopy can only be realized if the acquired signals Wiener filtering is another classical method that perare clear, stable, and free of noise. Unfortunately, this forms well under certain assumptions about signal stais rarely the case in practical applications. Raman sig- tionarity and noise properties. It can produce satisfactory nals are often weak, and their acquisition is sensitive to results, especially in laboratory settings, but its performany external factors such as temperature, laser fluctu- mance decreases significantly in more dynamic or unconations, photobleaching, sample heterogeneity, or even trolled environments [ 5, 6, 7, 8, 9, 10 ]. instrument drift. In recent years, attention has turned toward machine Obtaining a clean, accurate signal is critical for reliable learning and, in particular, deep learning, for denoising tasks. These approaches do not rely on handcrafted rules ICYRIME 2025: 10th International Conference of Yearly Reports on but instead learn directly from examples. This ability to I1n4f-o1r6m,2a0t2ic5s, Mathematics, and Engineering. Czestochowa, January capture complex, non-linear patterns from data has led to $ [e-mail] (C. Napoli) performance levels that surpass those of classical meth© 2025 Copyright for this paper by its authors. Use permitted under Creative Commons License ods in many domains. In particular, convolutional neural Attribution 4.0 International (CC BY 4.0). networks (CNNs) have proven efective for processing However, these methods depend on the choice of the structured data like time series and spectra. wavelet basis and thresholding strategy, which often

Recent contributions in this area have applied deep needs manual tuning. residual learning to denoising problems with encourag- Other researchers adopted Empirical Mode Decoming results. Residual networks learn to estimate the noise position (EMD), which is a fully data-driven technique component instead of reconstructing the entire signal, suitable for non-linear and non-stationary data [ 19 ]. The simplifying the learning task and improving convergence. main advantage of EMD is its capacity to adaptively sepaOne of the most successful architectures in this field is the rate noise from signal through decomposition into IntrinDnCNN model, originally developed for image denois- sic Mode Functions (IMFs). Nevertheless, its results can ing. Adaptations of this architecture to one-dimensional sufer from mode mixing, and the quality of denoising is signals have been proposed, including in biomedical and not always guaranteed, especially in cases where noise physical measurement contexts [ 11, 12, 13, 14, 15, 16 ]. is not additive or where the signal does not meet the

In this project, a discriminative learning model based envelope symmetry conditions. on the DnCNN structure is implemented. It uses parallel Wiener filtering has also been considered an efective convolutional branches to better learn noise characteris- solution for Raman signal denoising. For example, Bai et tics without assuming any specific origin or structure of al. [ 20 ] applied a modified Wiener filter to improve Rathe signal. This makes the model suitable for a wide range man signal quality in conditions with low signal-to-noise of applications, including Raman spectroscopy. Special ratio. This technique does not require prior experimental emphasis is placed on ensuring that the model remains data, which is an advantage, but its performance degrades lightweight, which is important for future integration in the presence of non-Gaussian noise, which is common into embedded systems or portable spectrometers used in real-world spectroscopic data. in field operations. In the last few years, the research community has

By focusing on generalization, eficiency, and minimal shifted toward deep learning techniques due to their abilassumptions, this study aims to contribute to the growing ity to automatically learn representations from raw data. ifeld of AI-assisted spectroscopy, where deep learning is The most basic models used convolutional neural netrapidly becoming a standard tool for signal interpretation works (CNNs) trained on labeled spectral datasets. For and preprocessing. example, Pan et al. [ 21 ] proposed a dual-path CNN that processes the signal in parallel branches, each specialized in detecting diferent noise features. This architecture 2. Related Work improves robustness against baseline shifts and peak distortion, but it increases the computational cost.

Earlier attempts to denoise Raman spectra primarily re- More advanced models such as UHRED (Unsupervised lied on wavelet-based methods [ 17, 18 ], but these were Hyperspectral Residual Encoder-Decoder) introduced by quickly surpassed by techniques better suited to non- Abdolghader et al. [ 22 ] combined denoising and seglinear, non-stationary signals, such as EMD [ 19 ]. Al- mentation in an unsupervised pipeline, demonstrating though EMD decomposes signals into intrinsic mode promising results for hyperspectral data. However, these functions (IMFs) without prior signal characterization, models are often tailored for imaging applications and its performance is limited by requirements such as sym- may not directly generalize to one-dimensional Raman metry in the upper and lower signal envelopes, which spectra without significant adaptation. are not always met in Raman data. A separate line of work has explored residual learning

Raman spectroscopy, due to its sensitivity and speci- for signal restoration. One of the most well-known archiifcity, has long been used as a key method for material tectures is the DnCNN [23], originally developed for imidentification. However, the presence of noise and base- age denoising but recently adapted for one-dimensional line fluctuations strongly limits its reliability. The scien- signals as well [24]. The residual learning principle altific community has proposed many denoising techniques lows the model to focus on learning only the noise comto overcome this challenge, starting from classical sig- ponent, which simplifies training and improves convernal processing methods and gradually moving towards gence. This approach has been particularly successful machine learning and deep learning approaches. in biomedical signals and time-series applications where

One of the most traditional approaches to Raman sig- precise peak localization is required. nal denoising has been based on wavelet transforms. In addition, some authors have explored hybrid methThese methods decompose the signal into multiple fre- ods, combining classical signal processing techniques quency components, allowing selective suppression of with deep learning to balance interpretability and perfornoise at various scales. For instance, Kumar et al. [ 17 ] mance. For example, Zhou et al. [25] designed a model and Chen et al. [ 18 ] used discrete wavelet transforms to that applies adaptive baseline correction before feeding smooth Raman signals while preserving spectral peaks. the signal into a neural network. These hybrid systems often achieve good results, but they can be sensitive to several normalization and baseline correction techniques, errors in the preprocessing stage. including Z-score normalization, max scaling, baseline

To summarize, although many strategies have been subtraction using polynomial fitting, and wavelet-based proposed, there is still no universally accepted solution background removal. While some of these methods profor Raman signal denoising. Classical methods often fail duced visually appealing results, they often introduced to generalize across diferent noise types and signal con- small distortions in peak shapes or amplitudes, which ditions. Deep learning models show great promise but could negatively afect the learning process. sometimes require large labeled datasets and careful tun- Among all tested methods, the most efective and roing. In this context, our work proposes a lightweight bust was a simple transformation: shifting the minimum parallel residual CNN, trained on synthetically noised value of each spectrum to zero. This method ensures that spectra, capable of generalizing across varying noise pat- the entire signal lies in the positive domain and removes terns and maintaining high peak fidelity even in distorted negative values, which are not expected in Raman intenbaselines. This contributes to improving the practical sity data. More importantly, this approach preserves the usability of Raman spectroscopy in both research and relative intensity of peaks, avoids rescaling artifacts, and applied contexts. maintains the original structure of the noise. This makes it easier for the neural network to distinguish noise from real spectral features. For this reason, minimum-shift 3. Dataset and Pre-Processing normalization was selected as the default pre-processing step for all experiments.

Finally, in order to make the data compatible with convolutional neural network layers, each input signal was reshaped into a three-dimensional tensor with the shape (samples, timesteps, 1). This format treats the Raman signal as a one-dimensional image with a single channel, allowing the model to apply 1D convolutions and learn local noise patterns efectively. This reshaping is a standard procedure when working with convolutional architectures in time-series or spectral signal processing tasks.

4. Model

The proposed denoising model is a parallel deep residual neural network architecture based on the DnCNN framework, specifically adapted for one-dimensional Raman spectral data. The core idea is to employ multiple independent branches, each learning to capture distinct noise patterns present in the input signal. This parallel configuration improves the model’s robustness and generalization, especially across datasets with diferent noise characteristics.

Each branch of the network processes the same input signal in parallel, applying a series of 1D convolutional layers with varying kernel sizes and dilation rates. This allows each branch to extract features at diferent temporal scales. The layers use LeakyReLU activation functions to maintain gradient flow and allow for learning non-linear transformations. Batch Normalization is included as an optional component to stabilize and speed up training, although experiments indicate that omitting it can sometimes yield better performance in this context.

To encourage generalization and reduce overfitting, L2 regularization is applied to the convolutional layers, with regularization strengths fine-tuned in the range of 1− 5 to 1− 6. Each branch outputs an intermediate estimate of the noise, and these outputs are averaged to form a combined noise prediction.

The final denoised signal is obtained by subtracting this aggregated noise estimate from the original input. This residual learning formulation focuses the model’s capacity on learning the noise component rather than reconstructing the full signal, which simplifies the learning task and improves convergence.

The model is compiled using the Adam optimizer, chosen for its eficiency and adaptability. The loss function is the Residual Sum of Squares (RSS), which emphasizes penalizing large errors in noise estimation. Additionally, Mean Squared Error (MSE) and Mean Absolute Error (MAE) are used as evaluation metrics during training and validation.

The training process is supported by a suite of callbacks, including: • ReduceLROnPlateau: Dynamically reduces the learning rate when performance plateaus. • EarlyStopping: Prevents overfitting by halting training when validation performance stops improving. • ModelCheckpoint: Saves the best-performing model during training. • TensorBoard: Provides real-time visualization of training metrics.

Overall, this architecture is designed to be lightweight, modular, and eficient, making it suitable not only for

Raman spectroscopy but also for other one-dimensional

denoising tasks in time-series analysis. denoising without signal distortion (Figures 4 and 5).

Quantitative evaluations involved peak detection accuracy and intensity prediction, as shown in Table 1. 5. Experiments and Results Peak localization accuracy consistently exceeded 81%, and peak intensity accuracy ranged from 78% to 92% The model was optimized through extensive testing. The depending on noise level. best-performing configuration includes depth settings Comparative results with prior work [ 21 ] (Table 2) of [ 17, 12, 7, 3 ], corresponding filter counts of [96, 64, demonstrate that our model achieves substantially lower 32, 96], kernel sizes of [ 5, 15, 30, 7 ], dilation rates of 5, RMSE and MAPE values, outperforming state-of-the-art no Batch Normalization, and L2 regularization between methods even under high-noise conditions. 1− 5 and 1− 6.

Among pre-processing strategies, shifting the minimum to zero led to the best results, achieving excellent

6. Conclusion

This paper proposes a parallel convolutional neural network model for denoising highly variable onedimensional signals, such as those encountered in Raman spectroscopy. Each network branch independently learns noise characteristics, and the final model combines these learnings for superior results. Pre-processing via minimum shifting, which preserves signal integrity, further enhances performance.

Experimental results demonstrate excellent qualitative and quantitative denoising performance across datasets, establishing the proposed method as a significant advancement over previous techniques.

7. Declaration on Generative AI

During the preparation of this work, the authors

used ChatGPT, Grammarly in order to: Grammar and spelling check, Paraphrase and reword. After using this tool/service, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content. 35–41 [1] S. Russo, S. Ahmed, I. E. Tibermacine, C. Napoli, Enhancing eeg signal reconstruction in cross-domain adaptation using cyclegan, in: Proceedings - 2024 International Conference on Telecommunications and Intelligent Systems, ICTIS 2024, 2024. doi:10.

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