# Optimization of denoising approaches in the context of ultra-fast LIBS imaging

Ruggero Guerrini, Cesar Alvarez-Llamas, Lucie Sancey, Vincent Motto-Ros, Ludovic Duponchel

► To cite this version:

Ruggero Guerrini, Cesar Alvarez-Llamas, Lucie Sancey, Vincent Motto-Ros, Ludovic Duponchel. Optimization of denoising approaches in the context of ultra-fast LIBS imaging. Spectrochimica Acta Part B: Atomic Spectroscopy, 2025, 227, pp.107167. 10.1016/j.sab.2025.107167. hal-04987255

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# Optimization of denoising approaches in the context of ultra-fast LIBS imaging

Ruggero Guerrini<sup>a</sup>, Cesar Alvarez-Llamas<sup>b,*</sup>, Lucie Sancey<sup>c</sup>, Vincent Motto-Ros<sup>b</sup>, Ludovic Duponchel<sup>a</sup>

## ARTICLE INFO

### Keywords:

LIBS imaging

Denosing methods

Elemental analysis

PCA

kHz LIBS

## ABSTRACT

Laser-Induced Breakdown Spectroscopy (LIBS) has emerged as a powerful analytical tool capable of providing multi-elemental information from a single laser pulse with minimal sample preparation. This technique generates a laser-induced, transient plasma on the sample surface, whose spectral emission is analyzed to determine its elemental composition. µLIBS-Imaging, a variant offering spatially resolved elemental analysis, holds promise for applications in diverse fields such as industry, geology, forensics, and biomedicine. Our drive to go ever faster and analyze increasingly larger areas of interest in samples now compels us to use kHz lasers for this elemental imaging. Despite its potential, implementing such lasers in µLIBS-imaging would face diverse challenges mainly related to weak plasma emission and signal-to-noise ratio (SNR) degradation, particularly when applied to delicate biological samples. This paper investigates methods to enhance SNR in fast µLIBS imaging, particularly for biomedical applications. We focus on denoising techniques suitable for high-frequency laser applications, comparing methods like Savitzky-Golay smoothing, Fast Fourier Transform, wavelet-based filtering, Whittaker Filtering, and Principal Component Analysis (PCA). Our strategy optimizes denoising parameters for specific elemental emission peaks, enhancing SNR for individual elements of interest. The results demonstrate significant improvements in data quality, paving the way for more accurate and efficient elemental imaging in complex biomedical specimens.

## 1. Introduction

Laser-Induced Breakdown Spectroscopy (LIBS) has gained attention in the analytical community due to its ability to provide simultaneous multi-elemental information from a single laser pulse with minimal sample preparation and no ambient requirements. This analytical technique uses short-laser pulses (typically in the order of nanoseconds or below) focused on a sample surface to obtain chemical information about its constituents. When the laser beam's fluence exceeds a specific threshold value, based on the material of the sample, a small amount of material is ablated from the surface, creating a transient plasma that emits specific spectral signatures resulting from the relaxation of the atoms, ions, or molecules presents in the laser-induced plasma. This spectral signature is then analyzed using a spectrograph to determine the sample's elemental composition. Furthermore, LIBS can detect all elements in the periodic table, with the capability to carry out in-lab,

stand-off [1], or in-situ [2] measurements with detection limits in the order of µg.g⁻¹. Moreover, thanks to the small size of the laser-sample interaction area, it is possible to provide a spatially resolved characterization of different surfaces, i.e., elemental imaging. With a lateral resolution in the order of a few µm, µLIBS-imaging is successfully employed in various fields, such as industry [3], geology [4], forensics [5], and biology [6,7], to name just a few. A further appeal for µLIBS-imaging is the analysis speed, which is currently mainly limited by the laser shooting rate. Currently, most of the µLIBS-imaging setups have lasers with a shooting rate lower than 100 Hz [6]. However, the use of kHz lasers could be a significant breakthrough for elemental imaging analysis. Nowadays, the use of kHz laser on LIBS is not widespread, although literature presents several examples mainly focused on industrial [8,9] or geological applications [10]. Using such sampling frequencies, kHz range, offers a significant benefit in terms of analysis time reduction, enabling mapping 1 million spectra - equivalent to 1 cm² with

<footnote><sup>a</sup> Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire de Spectroscopie pour Les Interactions, La Réactivité et L'Environnement, Lille 59000, France</footnote>

<footnote><sup>b</sup> Institut Lumière Matière UMR 5306, Université Lyon 1. CNRS, Villeurbanne, France</footnote>

<footnote><sup>c</sup> Université Grenoble Alpes, INSERM U1209, CNRS UMR 5309, Institute for Advanced Biosciences (IAB), Grenoble 38000, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: cesar.alvarez-llamas@univ-lyon1.fr (C. Alvarez-Llamas).</footnote>
a lateral resolution (i.e., shot-to-shot distance) of 10 µm - in roughly 17 min. Building on these advancements, µLIBS-Imaging at kHz rate is attracting the interest of new fields of application. In addition, it requires compact and transportable equipment, with no need for consumables, and reduced economic cost and environmental impacts, making it an interesting candidate to be implemented in fields combining research and routine requirements, such as biomedicine, where specimens can be incredibly diverse and complex, composed of multiple tissues such as bone tissue, muscular or blood vessels [6]. Nonetheless, its implementation has diverse challenges. Firstly, as a direct consequence of the reduction in the analysis time, the measure of elemental distribution maps with a considerable quantity of pixels (1 pixel in the elemental map corresponds to 1 spectrum) becomes easily achievable, resulting in an increase in the complexity of the data treatment process since the number of spectra would be increased in, at least, one order of magnitude. To address this challenge, new and more efficient tools are required; previous work has proposed different solutions, such as the use of novel artificial intelligence techniques, including Facebook libraries for clustering [11], or new mask-creation operations via logical relationships for mineral phase identification [10]. Moreover, to avoid compromising the lateral resolution of the analysis, it is crucial to minimize the induced thermal or stress damage due to laser-matter interaction, especially for the biological specimen, as they are typically more fragile than mineral or metal samples. Thus, low-energy laser pulses (1 mJ or lower) are recommended. Unfortunately, this approach results in a weaker plasma emission. Additionally, detectors capable of achieving an analysis rate in the kHz range are necessary. For kHz LIBS, two-dimensional sensors, such as sCMOS, are typically employed. However, the effective area of the sensor (sensor pixels) must be reduced to achieve the desired acquisition rate, reducing the light amount recorded. The combination of these factors inevitably causes the worsening of the signal-to-noise ratio (SNR) of the acquired spectra and, therefore, a decrease in the elemental image quality generated from them. The noise could strongly impact the quality and quantitative analysis of minor compounds, affecting the limit of detection (LOD). In biological sample analysis, this could reduce the capability of detecting specific minor compounds in the tissue that can have a relevant role in some diseases. Losing this information plays a decisive (negative) role in the study of bioclinical samples. Then, identifying and reducing the noise contributions affecting the analysis is of paramount importance. Numerous methods are available for reducing the influence of noise on acquired signals and enhancing the signal-to-noise ratio (SNR) in analytical measurements. One option is to optimize the instrumental hardware, such as the detector cooling system or adequate gain level selection, which can minimize the noise generated by the detector reading process. We can indeed always make efforts at the instrumental level to reduce noise, but ultimately, this remains quite limited in this particular framework, and therefore, another approach is required: using chemometric methods to clean up the signal as much as possible and improve the quality of the analytical information [12]. Overall, selecting a specific method for reducing noise and enhancing SNR depends on the nature of the data and the specific analytical application. In this context, denoising can be applied either spectrum by spectrum or across the entire dataset. In the first case, denoising can be applied almost in real time; however, if optimization is needed, especially for a heterogeneous sample, a complete spectral dataset is required. Quite intuitively, we can imagine that a denoising method based on analyzing the entire dataset will better understand the structure of the signals, and therefore perform more effectively in this filtering task. In the LIBS domain, the most commonly used methods for denoising are Savitzky-Golay smoothing, Fast Fourier Transform, wavelet-based filtering, and the Whittaker Filter (Whitsm), all based on working on each spectrum individually [13]. To complement these four widely used techniques, we propose also exploring Principal Component Analysis (PCA) in this denoising framework. It's worth noting that PCA has already been utilized in combination with other methods to explore LIBS imaging

datasets [14,15]; however, to our knowledge, this is the first time this approach has been applied for denoising purposes in the LIBS domain. In this paper, we compare different techniques for denoising with a focus on fast µLIBS-imaging for biomedical applications, particularly for analyzing endogenous and exogenous elements in tissue. Our approach is adapted to imaging applications: rather than seeking a global denoising method for the entire spectral range, we aim to optimize denoising parameters for specific elemental emission peaks. This targeted strategy allows us to enhance the Signal-to-Noise Ratio (SNR) for individual elements of interest, recognizing that different elements may require distinct denoising parameters or methods for optimal results.

## 2. Material and methods

### 2.1. LIBS experimental set-up

The LIBS experimental set-up comprises a kHz laser (Cobolt Tor XE, λ = 1064 nm) capable of achieving a shooting rate of 1000 Hz and the laser-focusing optics (x10 beam expander followed by an x5 objective). The sample is placed on a set of XYZ linear motorized stages to displace precisely the sample during the analysis. The elemental images presented in this work were recorded with a lateral resolution (i.e., shot-to-shot distance) of 10 µm, with a typical crater diameter around 7 µm. Each of them were composed of 1400 by 1500 pixels, derived from 2.1 million acquired spectra. The detection system is based on an Andor's iStar sCMOS sensor coupled to an Andor's Kymera Czerny-Turner spectrograph. The experimental conditions were fixed to 5 µs as integration time without delay time.

### 2.2. The sample of interest

Rat kidney was collected 1 h after intravenous injection of Au NP (size <10 µm). The sample was fixed in paraformaldehyde 4 % solution for 1 h, before epoxy-embedding following previously reported procedure [16]. The sample was split following the transversal axis. Then, the surface of the sample was polished before analysis.

### 2.3. Generation of chemical images from LIBS data

The typical µLIBS-imaging data processing workflow involves extracting the analytical signal from the spectra dataset. This analytical signal could be the emission line's maximum intensity, area, or net area for each element detected. Once this signal is extracted, it is used to create a chemical imaging map of the inspected sample. In this work, we use the net peak area as an analytical signal calculated as the signal region's mean minus the background region's mean.

In the sample presented in this work, three elements have been considered: P presents in the whole tissue; Fe, related to the blood vessels; and Au, an exogenous element due to the presence of gold nanoparticles. The purpose of this publication is, of course, not to provide an exhaustive exploration of this tissue but rather to demonstrate the validity of our approach on a set of elements with varying signal qualities within a single sample. Fig. 1a shows a visible image of the kidney analyzed in this study. On this same image, three specific positions (denoted as L1, L2, and L3) were randomly selected so that we could observe the associated LIBS spectra before and after applying denoising strategies. The raw spectra acquired at these three positions are shown in Fig. 1c. Fig. 1b, for its part, presents the integration images generated from the raw spectral data for four elements.

### 2.4. Denoising methods

As introduced before, we will compare 5 different methods to reduce noise from data while preserving important signal characteristics. The methods selected in this work reflect those commonly employed in various spectroscopic techniques, extending far beyond the scope of
<figure><img src="image_3.png" /><figcaption>Fig. 1. a) Optical Image of the analyzed sample. b) Elemental distribution for different elements: P (253 nm), Au (267 nm), Fe (274 nm). c) Spectra obtained from the three selected positions, along with the specific spectral regions corresponding to the elements of interest.</figcaption></figure>

LIBS. This is precisely why they are investigated here, as they have demonstrated good performance in denoising spectroscopic data.

### 2.4.1. Principal component analysis (PCA)

Principal Component Analysis [17] is a well-known method for the reduction of dimensionality, allowing a more straightforward representation and description of complex, multivariate datasets. The dataset X, applying PCA, is rewritten as a linear combination of the original variables to explain most of the variance, and it can be described as follows:

$$X = T.P^T + E$$

where T is the scores matrix, i.e., the projection of the original data into the low-dimensional space; P is the loadings matrix, and E is the residuals one. Because noise contributes to a small percentage of the total variance, reconstructing the original matrix after selecting a given number of the very first principal components (PCs) with the higher explained variance will potentially provide a denoised dataset. As can be seen, this denoising procedure applies to the entire dataset simultaneously. The entire optimization of such a denoising method lies in selecting an optimal number of principal components. Indeed, selecting too few components would risk losing part of the signal of interest, while

selecting too many would only introduce additional noise.

### 2.4.2. Savitzky-Golay smoothing

This method performs a least-squares fit of a low-degree polynomial to a moving window of data points, effectively smoothing the signal while potentially preserving its features.

The parameters to optimize the Savitzky-Golay smoothing are the width of the window, and the degree of polynomial function used for signal interpolation. This procedure applies independently to each spectrum of the dataset [18].

### 2.4.3. Fast Fourier Transform (FFT)

The Fast Fourier Transform (FFT) decomposes the original signal into a series of frequency components. It can also be shown that this method, like PCA, performs a decomposition of the spectra into a basis of orthogonal components, which in this case are sinusoids of different frequencies. Spectral noise is usually related to small fluctuations with high frequencies in the signal. Relevant signals are usually associated with lower frequencies with higher contributions. By transforming the spectra to the frequency domain, if noise has frequencies different from the interesting ones, reducing them to zero and applying the inverse FFT, it is possible to rebuild the signal, reducing the noise. This procedure also applies independently to each spectrum of the dataset [12].
### 2.4.4. Wavelet Threshold Denoising (WTD)

Wavelets [19] enables spectra decomposition at various levels, capturing high-frequency noise, low-frequency baselines, and intermediate components at different frequency levels. This multi-scale representation allows for analyzing different signal features at different levels of detail. Wavelet decomposition involves recursively applying a matrix of wavelet filter coefficients to the signal [12]. After decomposition, the small coefficients are typically related to noise, while the large coefficients are associated with the significant features. Removing or reducing the smallest coefficients makes it possible to reduce noise without affecting the main signal features. WTD (Wavelet Threshold Denoising) method has already been used in the LIBS domain by Schlenke et al. [17] as a spectral denoising tool. The parameters to optimize with this approach are the type of wavelet function, the decomposition level, and the threshold choice. The decomposition level determines the number of times the signal is decomposed into approximate and detailed components. The selection of the threshold is crucial and challenging. However, we used in this work the universal threshold method proposed by Donoho et al. [20].

The method involves three steps:

1. Apply the Wavelet transform with a decomposition level chosen in advance.

2. Select a proper threshold for each level.

3. Filter the coefficients below the threshold and reconstruct the signal with the inverse wavelet transform.

There are two main types of filtering, both evaluated in this work: hard and soft. With hard filtering, all the coefficients below the threshold are forced to be zero. Soft filtering reduces the coefficients by a given threshold [20]. Regarding the type of wavelet, we limited ourselves to Daubechies wavelets, which have proven effective in many spectroscopies beyond LIBS.

### 2.4.5. Whittaker smoothing

Considering the original signal as y and the smoothed one as z, Whittaker Smoothing [21] modifies the signal, balancing two conflicting objectives: (1) data fidelity and (2) roughness of z. This method is based on the use of the penalized least squares method to seek the series z that minimizes Q:

$$Q = S + \lambda R$$

where “S” is the discrepancy from the data, measured as the sum of squared differences $S = \sum_i (y_i - z_i)^2$; lambda, $\lambda$, is a user-chosen parameter; and R, roughness, defined as $R = \sum_i (z_i - z_{i-1})^2$. A larger $\lambda$ increases the weight of R in Q, resulting in a smoother z but potentially a poorer fit to the data, as the smoother z is, the more it will diverge from y. This method is particularly used in vibrational spectroscopy on data that are often especially noisy.

### 2.5. Figures of merit

One of the critical points for better selecting and optimizing the denoising method is the definition of a signal-to-noise ratio (SNR) criterion. Different methods for the calculations of the SNR are available to evaluate the quality of a spectral denoising procedure. The approach used in this paper is the calculation of SNR based on the spectra. It will be denoted SNR<sub>sp</sub> in this work. It is calculated in three steps considering a given element:

1. Estimation of the noise level: a specific spectral range is selected for the estimation. The 269.2-270.8 nm area is chosen in our case because it does not exhibit significant spectral contributions. Thus, for each spectrum in the dataset, the standard deviation of the measured values within this spectral range is calculated. This

dispersion provides an estimate of the noise level for a given spectrum. Then the mean of all these standard deviations is calculated, as a global estimation of noise in the dataset.

2. Estimation of the signal level: a spectral region around an emission line of an element of interest is selected. We calculate the average of these integration values for all the spectra in the dataset, retaining only those within the 99.99th percentile beforehand. This allows us to avoid biasing the estimation due to potentially outlier values while ensuring the detection of weak signals.

3. The SNR<sub>sp</sub> value is then calculated by taking the ratio of the two previously estimated values.

Beyond these SNR<sub>sp</sub> values, spectra and images can also be examined before and after correction to better understand the impact of such a method on both spectral and spatial levels.

## 3. Results and discussions

### 3.1. Denoising methods optimization

The following section will present the optimization for the different denoising methods. We want to show here that beyond selecting a given method, each one uses parameters that must be optimized to achieve the best denoising. Fig. 2 represents a schema summarizing the data treatment process used in this work. Typically, in the case of imaging results based on spectroscopic techniques, we generally carry out the denoising, before or after extracting the analytical signal. The denoising after extracting the analytical signal is based on the use of image treatment methods; however, in this work, we will only focus on denoising the spectral information before extracting the analytical signal.

As a reference point, the SNR<sub>sp</sub> values evaluated from the raw dataset are given in Table 1. In fact, we can see that the highest values naturally come from the elements with the highest average emission level, i.e., Au, across the entire dataset. These values will enable us to assess the effectiveness of the different denoising methods.

The proposed methods require an optimization process to obtain the optimum SNR<sub>sp</sub> in order to obtain the best image reconstruction possible, i.e., we have some a priori knowledge of the elements to be optimized, allowing us to evaluate the SNR improvement for each of the element's analytical signals separately. This optimization step would need to be redone if we manage spectral data from a new sample with a different composition.

### 3.2. Principal Component Analysis (PCA)

The PCA was applied to the entire dataset also considering the whole spectral domain. As previously stated, the denoised approach based on PCA is based on the fact that the first principal components (PCs) extracted reflect the chemical variances, and beyond a specific component, only noise is captured. Consequently, selecting an appropriate number of PCs is an essential optimization step. The number of PCs selected is optimized for each element based on the highest SNR improvement (ratio between the calculated SNR and the raw spectra SNR), which varies as a function of the number of retained PCs, as shown in Fig. 3a. We thus observe that the signal-to-noise ratio is improved by a factor of approximately 5 for the three elements when PCA is used, which is quite remarkable. Another way to look at it would be to say that, theoretically, the signal-to-noise ratio observed after this denoising could potentially be achieved with instrumentation 25 times slower, operating not in the kHz range but at 40 Hz. Beyond this initial observation, we must also highlight that an optimal number of different components is obtained for each element. As a result, optimal denoising is achieved for the elements P, Au, and Fe with a total number of principal components equal to 10, 9, and 23, respectively. This result is quite logical, as each one exhibits varying degrees of variance within the spectral dataset and is, by definition, described by a different number of
<figure><img src="image_4.png" /><figcaption>Fig. 2. The data analysis strategy.</figcaption></figure>

<table><caption>**Table 1**

SNR obtained from the raw spectra for the 3 elements into consideration.</caption><thead><tr><th></th><th>SNR (x 10<sup>2</sup>)</th></tr></thead><tbody><tr><td>P I <sub>253.5 nm</sub></td><td>1.19</td></tr><tr><td>Au I <sub>267.6 nm</sub></td><td>4.35</td></tr><tr><td>Fe II <sub>274.9 nm</sub></td><td>1.03</td></tr></tbody></table>

principal components. Beyond these signal-to-noise ratio values measured on the raw data and then on the potentially denoised data, it also seemed important to us to assess the relevance of a denoising strategy in terms of preserving the spectral information contained in the spectra. Indeed, such processing could, in extreme cases, distort or even eliminate an emission line of interest. Fig. 4 shows the evolution of the L1, L2, and L3 spectra, whose locations were presented in Fig. 1, before and after the application of a given denoising method. To be more precise, only the spectral regions of interest are considered for each element. The visual comparison of the spectra enables us to observe the denoising efficiency of PCA for all elements while preserving the associated emission lines, ensuring no distortion. At first glance, some readers might argue that, on the contrary, distortions are indeed observed when PCA is applied for denoising. We are not actually referring to distortions across the entire spectrum but only to the emission line related to the element of interest, which is quite different. Thus, if we refer to the emission lines of P, Au, and Fe at 253.56 nm, 267.6 nm, and 274.9 nm respectively, we observe that, compared to the raw data, their profiles are preserved after PCA denoising. Regarding the emission line observed around 253.5 nm in the raw data, it is not inconsistent for it to disappear after PCA denoising. Indeed, this line is not associated with phosphorus but with another element, which is likely represented by principal components beyond the optimal number chosen for denoising in this specific context of generating a phosphorus image. Building on these results, it is worth pausing to consider the

applicability of this denoising approach to a dataset of this scale, comprising 2.1 million spectra. The computations, performed in a MATLAB environment, required in our case 23 GB of RAM, which remains entirely feasible within the computational frameworks used in spectroscopic imaging. Should memory constraints arise for certain users, adopting an HDF5 data format is recommended, as it allows for sequential access to smaller subsets of the spectral dataset as needed. Under such conditions, an alternative implementation of the PCA algorithm, such as incremental PCA, should be considered to accommodate this segmented data exploration [22].

### 3.3. Savitzky-Golay smoothing

The parameters to optimize for the Savitzky-Golay smoothing are the polynomial order and the window size. The first and second orders were tested, while the window lengths tested were between 3 and 31 (with a step of 2). All combinations of these two parameters have thus been studied. When examining the results in Fig. 3b and c, it is noticeable that the signal-to-noise ratio tends to stabilize when the window size reaches approximately 20, regardless of the polynomial order for Au. The improvement in the signal-to-noise ratio is, however, relatively limited in this case to a value of approximately 2, whereas it was 5 for PCA. The signal-to-noise ratio appears to increase consistently for the elements P and Fe, but this trend does not reflect a true improvement in spectral quality in terms of noise. Indeed, in Fig. 4, we observe completely distorted emission lines for the elements of interest following such correction, which is unacceptable. Therefore, Savitzky-Golay smoothing is not optimal for our LIBS imaging data. This approach is indeed very effective for vibrational spectroscopies, for example, but the bands observed are much broader than the noise structure. This is absolutely not the case in LIBS, where we observe very sharp emission lines.
<figure><img src="image_5.png" /><figcaption>Fig. 3. Evolution of the $SNR_{denoised}$ dataset /$SNR_{raw}$ dataset for the different methods.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 4. Denoised Spectra for the SNR optimal values with all the studied denoising methods. Fe spectrum corresponds to the point-of-interest L1, Au to L2, and P to the point-of-interest L3, denoted in Fig. 1.</figcaption></figure>

### 3.4. Fast Fourier Transform (FFT)

Once the signal is decomposed into the frequency domain with the FFT approach, the frequencies that are not related to the signal of interest are set to zero. To achieve this, we calculate the Power Spectrum Density (PSD) and set all frequencies below a predetermined threshold value to zero to eliminate all frequencies that do not significantly contribute to the signal. The different values used as thresholds are quantiles of the PSD. Various quantiles, ranging from 0.05 to 0.85 with a step of 0.05, were evaluated. Fig. 3d shows an optimal $SNR_{sp}$ value of 1.06 for a 0.70 quantile threshold regardless of the element considered. Consequently, the improvement in the signal-to-noise ratio is very minimal, if not negligible, which is also evident in the spectra shown in Fig. 4.

### 3.5. Wavelet Threshold Denoising (WTD)

The wavelet family used in this case was db4 (i.e., Daubechies 4), with a hard and soft denoising approach. We selected this wavelet family as it has demonstrated its effectiveness in numerous spectroscopic techniques [23,24]. We evaluated up to 4 decomposition levels for both hard and soft denoising because going further in the decomposition introduces artifacts in the spectra. Fig. 3e and f present a situation quite comparable to the previously introduced method. For both strategies, the signal-to-noise ratio consistently increases with the level of decomposition, though the improvement remains modest, barely reaching 2.5. Even worse, Fig. 4 shows that applying such a denoising method removes nearly all of the chemical information originally present in the spectra.

### 3.6. The Whittaker smoothing

The lambda value was optimized in this case, ranging from 1 to 400. Fig. 3g demonstrates that we quickly reached a plateau in the improvement of the signal-to-noise ratio for all three elements of interest. This improvement remains limited, as it averages around 2 times. It can be observed in Fig. 4 that, even though the denoised spectra using this approach appear significantly better than those obtained for SG, FFT, and WTD, the emission lines are noticeably broadened compared to the raw data.

Based on these results, we can unequivocally state that the PCA-

based denoising procedure is undoubtedly more suited for LIBS imaging. This is a particularly interesting finding, as the other techniques studied here generally perform quite well in the context of other spectroscopic methods. This can, of course, be explained by the specific nature of LIBS data, especially the presence of particularly narrow emission lines. We also emphasize the importance of optimizing the number of components for each element. The final step of this work now involves observing the effects of the denoising procedure using PCA on the integration images. Fig. 5 thus presents a comparison of the integration images obtained from the raw spectra and the spectra denoised using PCA for the three elements considered. Starting with a global observation of this figure, we can see that the largest differences are observed for Fe and P. The differences are indeed less noticeable for Au. This is naturally explained by the fact that the weakest signals are associated with Fe and P, and it is precisely under these conditions that an increase in the signal-to-noise ratio has a significant impact. Arrows have also been added to these images to highlight details or areas that differ significantly between them and will therefore be discussed in greater detail. If we first examine the iron maps, we can immediately observe an overestimation of concentrations when raw spectra are used, as seen, for example, in positions a vs. a' and b vs. b'. This iron originates from blood and is particularly present in the vascularized areas of the organ. Therefore, it cannot be found outside the organ or at its center, which is much more consistent in the image obtained after PCA denoising. A low dynamic range and very low contrast are also observed in the iron image derived from the raw spectra—values that are significantly improved after denoising, allowing the observation of previously unseen details (d vs. d', e vs. e', and f vs. f'). Fairly similar observations can be made for P. However, these differences are less striking, as we know that phosphorus is present in numerous cells and is distributed throughout the organ. As a result, overestimations of phosphorus concentrations are once again observed outside the organ and at its center (g vs. g', i vs. i', and l vs. l') when raw spectra are used. Imperceptible details from the raw data are also revealed when the spectra are denoised (h vs. h', j vs. j' and k vs. k'). Regarding gold, our biological understanding of the issue allows us to state that it can only be present at the periphery of the organ. As a result, an overestimation of concentrations is observed both outside the organ and at its center, which is much more consistent when denoised spectra are used. Through these three elements with varying concentration ranges and locations within this complex organ, we were able to demonstrate that applying PCA as a
<figure><img src="image_7.png" /><figcaption>Fig. 5. Comparison between the original and denoised elemental distribution maps for Fe (274.9 nm), P (253.5 nm) and Au (267.6 nm).</figcaption></figure>

denoising method generates elemental images with improved contrast, greater dynamic range, and, most importantly, reduced bias, allowing us to better highlight the biological reality of the sample after processing.

4. Conclusions

The use of new experimental approaches that enable higher
throughput and higher resolution analysis makes the parallel develop-
ment of new chemometric tools mandatory. As the complexity and size
of spectral data increases - with hypercubes that can hold millions of
spectra - it is necessary to develop algorithms and workflows for spectral
processing to handle, analyze, and extract analytical information from
these data. In this work, we highlight the application of kHz µLIBS-im-
aging for the analysis of samples of bio-clinical interest, with a focus on a
comparative evaluation of 5 different denoising methods. Furthermore,
to our knowledge, this research applies principal component analysis
(PCA) and Whittaker Smoothing to LIBS data for the first time, opening

new ways to improve the accuracy of such analyses. The results shows
that PCA is by far the most effective method in this specific LIBS
framework, offering a better enhancement than the other methods.
Specifically, PCA provides an important SNR enhancement of approxi-
mately 5 times for the three elements under study compared to the raw
data; moreover, no distortion of the emission line of a given element has
been found, unlike the other denoising methods studied. In this work,
PCA was applied to the entire available spectral range, but in more
delicate cases, we could consider using the restricted range around the
emission line of interest for the PCA calculation. We certainly evaluated
this option, but we did not observe any significant improvement, at least
for this particular dataset. In conclusion, this enhancement in the quality
of the kHz µLIBS-imaging highlights the PCA value for the data treat-
ment of LIBS-based applications, particularly where the experimental
conditions limit the quality of spectral data.
CRediT authorship contribution statement

**Ruggero Guerrini:** Writing – original draft, Software, Methodology, Formal analysis, Data curation, Conceptualization. **Cesar Alvarez-Llamas:** Writing – review & editing, Writing – original draft, Supervision, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization. **Lucie Sancey:** Writing – review & editing, Resources, Methodology, Conceptualization. **Vincent Motto-Ros:** Writing – review & editing, Visualization, Validation, Supervision, Resources, Funding acquisition. **Ludovic Duponchel:** Writing – review & editing, Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Cesar Alvarez Llamas reports financial support was provided by Horizon Europe. Vincent Motto-Ros reports financial support was provided by French National Research Agency. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The project leading to this application was supported by the European Union's Horizon Europe Research and Innovation Program under the MSCA Postdoctoral Fellowships 2022, with agreement number 101106090; by the French Government "France 2030" initiative, under the DIADEM program managed by the "Agence Nationale de la Recherche" (ANR-22-PEXD-0014, "Libelul") and the "French Agence Nationale de la Recherche" (ANR-20-CE17-0021 "dIAg-EM", and "Micro-Q-Li" ANR-20-CE05-0015)

Data availability

Data will be made available on request.

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