Adaptive wavelet transform suppresses background and noise for quantitative analysis by Raman spectrometry

A LIBS spectrum baseline correction method based on the non-parametric prior penalized least squares algorithm

Laser-induced breakdown spectroscopy (LIBS) has become a popular element analysis technique because of its real-time multi-element detection and non-damage advantages. However, due to factors such as laser-substance interaction and the experimental environment, the measured LIBS spectrum signal contains a continuous background, severely influencing spectrum analysis. In this paper, we propose a LIBS spectrum baseline correction method based on the non-parametric prior penalized least squares (NPPPLS) algorithm. Compared with the traditional Penalized Least Squares (PLS) method, improvements have been made in two aspects. On the one hand, a new weight method with faster convergence is proposed. On the other hand, we combine the Adam algorithm and introduce the RMSE of the baseline correction result at the previous time to constrain the update of the balance parameter, which enables the balance parameter to be adjusted adaptively and no parameter prior is required. The simulation results show that the proposed NPPPLS algorithm can achieve excellent correction results, even with no parametric priors. In addition, the performance of the NPPPLS algorithm is not affected by the initial value of the balance parameter, and the stability and robustness are significantly improved. Finally, we conducted baseline correction of the experimental LIBS spectrum and performed univariate and multivariate analyses. The results show that the quantitative analysis accuracy is improved after baseline correction, and the correlation coefficient R2 of different elements obtained by the extreme learning machine method of multivariate analysis can reach 0.99, demonstrating a better quantitative analysis result. The simulation and experimental results verify the excellent performance of the proposed NPPPLS algorithm, which can be effectively used to improve the accuracy of quantitative analysis. In addition, this method is also expected to be used for baseline correction of the Raman spectrum, near-infrared spectrum and so on.

An intuitive approach for spike removal in Raman spectra based on peaks' prominence and width

BACKGROUND

Raman spectroscopists are familiar with the challenge of dealing with spikes caused by cosmic rays. These artifacts may lead to errors in subsequent data processing steps, such as for example calibration, normalization or spectral search. Spike removal is therefore a fundamental step in Raman spectral data pre-treatment, but access to publicly accessible code for spike removal tools is limited, and their performance for spectra correction often unknown. Therefore, there is a need for development and testing open-source and easy-to-implement algorithms that improve the Raman data processing workflow.

RESULTS

In this work, we present and validate two approaches for spike detection and correction in Raman spectral data from graphene: i) An algorithm based on the peaks' widths and prominences and ii) an algorithm based on the ratio of these two peak features. The first algorithm provides an efficient and reliable approach for spike detection in real and synthetic Raman spectra by imposing thresholds on the peaks' width and prominence. The second approach leverages the prominence/width ratio for outlier detection. It relies on the calculation of a limit of detection based on either one or several spectra, enabling the automatic identification of cosmic ray and low-intensity noise-originated spikes alike. Both algorithms detect low-intensity spikes down to at least ≈10% of the highest Raman peak of spectra with different noise levels. To address their limitations and prove their versatility, the algorithms were further tested in Raman spectra from calcite and polystyrene.

SIGNIFICANCE

Our intuitive, open-source algorithms have been validated and allow automatic correction for a given set of samples. They do not require any pre-processing steps such as calibration or baseline subtraction, and their implementation with Python libraries is computationally efficient, allowing for immediate utilization within existing open-source packages for Raman spectra processing.

Deep neural network: As the novel pipelines in multiple preprocessing for Raman spectroscopy

Raman spectroscopy is a kind of vibrational method that can rapidly and non-invasively gives chemical structural information with the Raman spectrometer. Despite its technical advantages, in practical application scenarios, Raman spectroscopy often suffers from interference, such as noises and baseline drifts, resulting in the inability to acquire high-quality Raman spectroscopy signals, which brings challenges to subsequent spectral analysis. The commonly applied spectral preprocessing methods, such as Savitzky-Golay smooth and wavelet transform, can only perform corresponding single-item processing and require manual intervention to carry out a series of tedious trial parameters. Especially, each scheme can only be used for a specific data set. In recent years, the development of deep neural networks has provided new solutions for intelligent preprocessing of spectral data. In this paper, we first creatively started from the basic mechanism of spectral signal generation and constructed a mathematical model of the Raman spectral signal. By counting the noise parameters of the real system, we generated a simulation dataset close to the output of the real system, which alleviated the dependence on data during deep learning training. Due to the powerful nonlinear fitting ability of the neural network, fully connected network model is constructed to complete the baseline estimation task simply and quickly. Then building the Unet model can effectively achieve spectral denoising, and combining it with baseline estimation can realize intelligent joint processing. Through the simulation dataset experiment, it is proved that compared with the classic method, the method proposed in this paper has obvious advantages, which can effectively improve the signal quality and further ensure the accuracy of the peak intensity. At the same time, when the proposed method is applied to the actual system, it also achieves excellent performance compared with the common method, which indirectly indicates the effectiveness of the Raman signal simulation model. The research presented in this paper offers a variety of efficient pipelines for the intelligent processing of Raman spectroscopy, which can adapt to the requirements of different tasks while providing a new idea for enhancing the quality of Raman spectroscopy signals.

Machine Learning Analysis of Raman Spectra To Quantify the Organic Constituents in Complex Organic-Mineral Mixtures

Important decisions in local agricultural policy and practice often hinge on the soil's chemical composition. Raman spectroscopy offers a rapid noninvasive means to quantify the constituents of complex organic systems. But the application of Raman spectroscopy to soils presents a multifaceted challenge due to organic/mineral compositional complexity and spectral interference arising from overwhelming fluorescence. The present work compares methodologies with the capacity to help overcome common obstacles that arise in the analysis of soils. We created conditions representative of these challenges by combining varying proportions of six amino acids commonly found in soils with fluorescent bentonite clay and coarse mineral components. Referring to an extensive data set of Raman spectra, we compare the performance of the convolutional neural network (CNN) and partial least-squares regression (PLSR) multivariate models for amino acid composition. Strategies employing volume-averaged spectral sampling and data preprocessing algorithms improve the predictive power of these models. Our average test R2 for PLSR models exceeds 0.89 and approaches 0.98, depending on the complexity of the matrix, whereas CNN yields an R2 range from 0.91 to 0.97, demonstrating that classic PLSR and CNN perform comparably, except in cases where the signal-to-noise ratio of the organic component is very low, whereupon CNN models outperform. Artificially isolating two of the most prevalent obstacles in evaluating the Raman spectra of soils, we have characterized the effect of each obstacle on the performance of machine learning models in the absence of other complexities. These results highlight important considerations and modeling strategies necessary to improve the Raman analysis of organic compounds in complex mixtures in the presence of mineral spectral components and significant fluorescence.

Quantitative analysis of heavy metals in soil by X-ray fluorescence with PCA-ANOVA and support vector regression

Heavy metal concentration is an important index for evaluating soil pollution. It is of great significance to measure the trace element content accurately for green agriculture development. In order to detect the trace element content accurately, a new prediction framework including pre-processing, signal extraction, feature selection and decision-making was proposed. The energy dispersive X-ray fluorescence (ED-XRF) spectra of 57 national standard soil samples were investigated based on the proposed methods. Firstly, an innovative background deduction method called iterative adaptive window empirical wavelet transform (IAWEWT) was introduced to extract effective counts of characteristic peaks, and the proposed approach was validated by the coefficient of determination (R²) of the instrumental calibration curve compared with two other conventional methods. Secondly, principal component analysis (PCA) was combined with the analysis of variance (ANOVA) for variable selection optimization of the ED-XRF spectrum. After PCA feature extraction and ANOVA variable selection treatment, the optimum number of principal components for V, Cr, Cu, Zn, Mo, Cd and Pb were determined to be 7, 15, 4, 4, 4, 5 and 12 respectively. Furthermore, the support vector regression (SVR) model was adopted for heavy metal estimation. The evaluation indices included R² and root mean square error (RMSE). It was demonstrated that the predictive capabilities of seven heavy metal elements were improved substantially for elemental analysis by the proposed PCA-ANOVA-SVR model, with excellent results for V, Cr, Cu, Zn, Mo, Cd and Pb estimates, and the R² values were 0.993, 0.996, 0.999, 0.999, 0.997, 0.998 and 0.998 respectively. Therefore, the new framework proposed in this paper can effectively eliminate redundant features and determine the concentration of trace elements in soil. It provides an effective alternative for the quantitative analysis of X-ray fluorescence spectrometry.

Spectral denoising based on Hilbert–Huang transform combined with F-test

Due to the influence of uncontrollable factors such as the environment and instruments, noise is unavoidable in a spectral signal, which may affect the spectral resolution and analysis result. In the present work, a novel spectral denoising method is developed based on the Hilbert–Huang transform (HHT) and F-test. In this approach, the original spectral signal is first decomposed by empirical mode decomposition (EMD). A series of intrinsic mode functions (IMFs) and a residual (r) are obtained. Then, the Hilbert transform (HT) is performed on each IMF and r to calculate their instantaneous frequencies. The mean and standard deviation of instantaneous frequencies are calculated to further illustrate the IMF frequency information. Third, the F-test is used to determine the cut-off point between noise frequency components and non-noise ones. Finally, the denoising signal is reconstructed by adding the IMF components after the cut-off point. Artificially chemical noised signal, X-ray diffraction (XRD) spectrum, and X-ray photoelectron spectrum (XPS) are used to validate the performance of the method in terms of the signal-to-noise ratio (SNR). The results show that the method provides superior denoising capabilities compared with Savitzky–Golay (SG) smoothing.

A Spatial-Temporal Analysis of Cellular Biopolymers on Leaf Blight-Infected Tea Plants Using Confocal Raman Microspectroscopy

The objective of the present study was to characterize the temporal and spatial variation of biopolymers in cells infected by the tea leaf blight using confocal Raman microspectroscopy. We investigated the biopolymers on serial sections of the infection part, and four sections corresponding to different stages of infection were obtained for analysis. Raman spectra extracted from four selected regions (circumscribing the vascular bundle) were analyzed in detail to enable a semi-quantitative comparison of biopolymers on a micron-scale. As the infection progressed, lignin and other phenolic compounds decreased in the vascular bundle, while they increased in both the walls of the bundle sheath cells as well as their intracellular components. The amount of cellulose and other polysaccharides increased in all parts as the infection developed. The variations in the content of lignin and cellulose in different tissues of an individual plant may be part of the reason for the plant's disease resistance. Through wavelet-based data mining, two-dimensional chemical images of lignin, cellulose and all biopolymers were quantified by integrating the characteristic spectral bands ranging from 1,589 to 1,607 cm^-1, 1,087 to 1,100 cm^-1, and 2,980 to 2,995 cm^-1, respectively. The chemical images were consistent with the results of the semi-quantitative analysis, which indicated that the distribution of lignin in vascular bundle became irregular in sections with severe infection, and a substantial quantity of lignin was detected in the cell wall and inside the bundle sheath cell. In serious infected sections, cellulose was accumulated in vascular bundles and distributed within bundle sheath cells. In addition, the distribution of all biopolymers showed that there was a tylose substance produced within the vascular bundles to prevent the further development of pathogens. Therefore, confocal Raman microspectroscopy can be used as a powerful approach for investigating the temporal and spatial variation of biopolymers within cells. Through this method, we can gain knowledge about a plant's defense mechanisms against fungal pathogens.

Baseline correction method based on improved adaptive iteratively reweighted penalized least squares for the x-ray fluorescence spectrum

To solve the problem of baseline drift in the detection of soil samples by x-ray fluorescence spectrum, an improved adaptive iterative weighted penalized least squares (IairPLS) method is proposed to estimate the baseline of x-ray fluorescence spectrum signals. We improved the original exponential weight function to solve the problem of baseline underestimation caused by adaptive iterative weighted penalized least squares. The improved function effectively reduces the risk of baseline underestimation and speeds up the weighting process, achieving good results. In this paper, the MC simulation spectrum and soil real analysis spectrum are used to verify the performance of the algorithm. Finally, the algorithm is compared with previous penalized least squares methods (asymmetric least squares, adaptive iterative reweighted penalized least squares, and multiple constrained reweighted penalized least squares), with the results showing that the proposed method has the least root-mean-square error after baseline correction for optimal smoothing parameters λ and the best relative error of baseline estimation accuracy. Meanwhile, the IairPLS method can effectively improve the quantitative analysis ability of the x-ray fluorescence spectrum. The proposed method can be successfully applied to the actual x-ray fluorescence spectrum, which provides a powerful basis for quantitative analysis.

ISREA: An Efficient Peak-Preserving Baseline Correction Algorithm for Raman Spectra

A critical step in Raman spectroscopy is baseline correction. This procedure eliminates the background signals generated by residual Rayleigh scattering or fluorescence. Baseline correction procedures relying on asymmetric loss functions have been employed recently. They operate with a reduced penalty on positive spectral deviations that essentially push down the baseline estimates from invading Raman peak areas. However, their coupling with polynomial fitting may not be suitable over the whole spectral domain and can yield inconsistent baselines. Their requirement of the specification of a threshold and the non-convexity of the corresponding objective function further complicates the computation. Learning from their pros and cons, we have developed a novel baseline correction procedure called the iterative smoothing-splines with root error adjustment (ISREA) that has three distinct advantages. First, ISREA uses smoothing splines to estimate the baseline that are more flexible than polynomials and capable of capturing complicated trends over the whole spectral domain. Second, ISREA mimics the asymmetric square root loss and removes the need of a threshold. Finally, ISREA avoids the direct optimization of a non-convex loss function by iteratively updating prediction errors and refitting baselines. Through our extensive numerical experiments on a wide variety of spectra including simulated spectra, mineral spectra, and dialysate spectra, we show that ISREA is simple, fast, and can yield consistent and accurate baselines that preserve all the meaningful Raman peaks.

Baseline correction method based on improved asymmetrically reweighted penalized least squares for the Raman spectrum

We present a baseline correction method based on improved asymmetrically reweighted penalized least squares (IarPLS) for the Raman spectrum. This method utilizes a new S-type function to reduce the risk of baseline overestimation and speed up the reweighting process. Simulated spectra with different levels of noise and measured spectra with strong fluorescence background from different samples are used to validate the performance of the proposed algorithm. Considering the drawbacks of the weighting rules for the asymmetrically reweighted penalized least squares (arPLS) method, we adapt an inverse square root unit (ISRU) function, which performs well in baseline correction. Compared with previous penalized least squares methods, such as asymmetric least squares, adaptive iteratively reweighted penalized least squares, and arPLS, experiments with the simulated Raman spectra have confirmed that the proposed method yields better outcomes. Experiments with the measured Raman spectra show that the IarPLS method can improve real Raman spectra within 20 ms. The results show that the proposed method can be successfully applied to the practical Raman spectrum as a strong basis for quantitative analysis.

TOGA feature selection and the prediction of mechanical properties of paper from the Raman spectra of unrefined pulp

Process-monitoring laboratories in the pulp and paper industry generally use a combination of wet chemical analyses and physical measurements to certify the fitness of a production pulp for a specific end-use. These laboratory tests require time and the effort of trained personnel, limiting their utility for real-time process control. Here we show that Raman probes of unrefined cellulosic pulps, well-suited to the online measurement of in-process materials, can predict the quality attributes of manufactured papers. The accuracy of prediction improves when the covariance is modelled in a reduced measurement space selected by a data-driven, feature-selection technique referred to as a Template Oriented Genetic Algorithm (TOGA). TOGA, combined with discrete wavelet transform (DWT), isolates functional-group features that correlate best with mechanical properties paper derived from refined pulp. Paper makers refine market pulps to build sheet strength using a beating process that decreases freeness as it increases fibre-fibre bonding. Methods demonstrated here predict manufactured sheet properties obtainable after any specified degree of refining from the Raman spectrum of an unrefined pulp. This analysis capacity will enable both vendors of market pulp and makers of sheet paper to specify in advance the amount of beating required to produce a desired product, thereby saving cost and conserving resources.

An Effective Prediction Approach for Moisture Content of Tea Leaves Based on Discrete Wavelet Transforms and Bootstrap Soft Shrinkage Algorithm

The traditional method used to determine the moisture content of tea leaves is time consuming and destructive. To address this problem, an effective and non-destructive prediction method based on near-infrared spectroscopy (NIRS) is proposed in this paper. This new method combines discrete wavelet transforms (DWT) with the bootstrap soft shrinkage algorithm (BOSS). To eliminate uninformative or interfering variables, DWT is applied to remove the noise in the spectral data by decomposing the origin spectrum into six layers. BOSS is used to select informative variables by reducing the dimensions of the sub-layers’ reconstruction spectrum. After selecting the effective variables using DWT and BOSS, a prediction model based on partial least squares (PLS) is built. To validate effectiveness and stability of the prediction model, full-spectrum PLS, genetic algorithm PLS (GA-PLS), and interval PLS (iPLS) were compared with the proposed method. The experiment results illustrate that the proposed prediction model outperforms the other classical models considered in this study and shows promise for the prediction of the moisture content in Yinghong No. 9 tea leaves.

Quantitative visualization of subcellular lignocellulose revealing the mechanism of alkali pretreatment to promote methane production of rice straw

BACKGROUND

As a renewable carbon source, biomass energy not only helps in resolving the management problems of lignocellulosic wastes, but also helps to alleviate the global climate change by controlling environmental pollution raised by their generation on a large scale. However, the bottleneck problem of extensive production of biofuels lies in the filamentous crystal structure of cellulose and the embedded connection with lignin in biomass that leads to poor accessibility, weak degradation and digestion by microorganisms. Some pretreatment methods have shown significant improvement of methane yield and production rate, but the promotion mechanism has not been thoroughly studied. Revealing the temporal and spatial effects of pretreatment on lignocellulose will greatly help deepen our understanding of the optimization mechanism of pretreatment, and promote efficient utilization of lignocellulosic biomass. Here, we propose an approach for qualitative, quantitative, and location analysis of subcellular lignocellulosic changes induced by alkali treatment based on label-free Raman microspectroscopy combined with chemometrics.

RESULTS

Firstly, the variations of rice straw induced by alkali treatment were characterized by the Raman spectra, and the Raman fingerprint characteristics for classification of rice straw were captured. Then, a label-free Raman chemical imaging strategy was executed to obtain subcellular distribution of the lignocellulose, in the strategy a serious interference of plant tissues' fluorescence background was effectively removed. Finally, the effects of alkali pretreatment on the subcellular spatial distribution of lignocellulose in different types of cells were discovered.

CONCLUSIONS

The results demonstrated the mechanism of alkali treatment that promotes methane production in rice straw through anaerobic digestion by means of a systemic study of the evidence from the macroscopic measurement and Raman microscopic quantitative and localization two-angle views. Raman chemical imaging combined with chemometrics could nondestructively realize qualitative, quantitative, and location analysis of the lignocellulose of rice straw at a subcellular level in a label-free way, which was beneficial to optimize pretreatment for the improvement of biomass conversion efficiency and promote extensive utilization of biofuel.

A spectral recovery method for Raman spectroscopy utilizing prior datasets

Spectral-based method has been widely used for the qualitative and quantitative analysis of different substances in various fields. The spectral recovery method is a crucial role in the spectral-based method, which can save the measurement cost and computation time in measuring. In this paper, we introduce a simple and reliable spectral recovery method base on prior datasets, which can tolerate substantial spectral noise. The method has been successfully applied in the quantitative analysis of the pharmaceutical mixture. The SNR of the recovery spectra can be increased by ~100 times.

Baseline correction method based on doubly reweighted penalized least squares

The spectrum acquired on the optical instrument usually contains the pure spectrum and undesirable components such as baseline and random noise. However, the intensity of the baseline, which seriously submerges the spectrum, is the primary limitation of spectral applications. Thus, baseline correction has become one of the most significant challenges for spectral applications. In this paper, we propose a doubly reweighted penalized least squares method to estimate the baseline. This method utilizes the first-order derivative of the original spectrum and established spectrum as a constraint of similarity. Meanwhile, the doubly reweighted strategy achieves a better effort. Considering the drawbacks of the weighting rules for the adaptive iteratively reweighted penalized least squares method, we adapt a boosted weighting rule based on the softsign function, which performs well when the spectrum contains high noise. The simulated results confirm that the proposed method yields better outcomes. The proposed method can be applied to Raman and near-infrared spectra as well, and the result shows that it can estimate various kinds of baselines effectively.

An Adaptive and Fully Automated Baseline Correction Method for Raman Spectroscopy Based on Morphological Operations and Mollification

Baseline drift is a commonly identified and severe problem in Raman spectra, especially for biological samples. The main cause of baseline drift in Raman spectroscopy is fluorescence generated within the sample. If left untreated, it will affect the following qualitative or quantitative analysis. In this paper, an adaptive and fully automated baseline estimation algorithm based on iteratively averaging morphological opening and closing operations is presented. The proposed method is able to deal with different shapes and amplitudes of baselines. It is tested on both simulated and experimental Raman spectra. Comparison of the proposed method with other morphology-based methods and a well-developed penalized least squares-based method is made. The results demonstrate the superior performance of the proposed method and its advantages-in terms of accuracy, adaptivity, and computing speed-over other algorithms. In general, this method can also be applied to other spectroscopic data or other types of one-dimensional data.

Raman Spectroscopy for Pharmaceutical Quantitative Analysis by Low-Rank Estimation

Raman spectroscopy has been widely used for quantitative analysis in biomedical and pharmaceutical applications. However, the signal-to-noise ratio (SNR) of Raman spectra is always poor due to weak Raman scattering. The noise in Raman spectral dataset will limit the accuracy of quantitative analysis. Because of high correlations in the spectral signatures, Raman spectra have the low-rank property, which can be used as a constraint to improve Raman spectral SNR. In this paper, a simple and feasible Raman spectroscopic analysis method by Low-Rank Estimation (LRE) is proposed. The Frank-Wolfe (FW) algorithm is applied in the LRE method to seek the optimal solution. The proposed method is used for the quantitative analysis of pharmaceutical mixtures. The accuracy and robustness of Partial Least Squares (PLS) and Support Vector Machine (SVM) chemometric models can be improved by the LRE method.

Collaborative Penalized Least Squares for Background Correction of Multiple Raman Spectra

Although Raman spectroscopy has been widely used as a noninvasive analytical tool in various applications, backgrounds in Raman spectra impair its performance in quantitative analysis. Many algorithms have been proposed to separately correct the background spectrum by spectrum. However, in real applications, there are commonly multiple spectra collected from the close locations of a sample or from the same analyte with different concentrations. These spectra are strongly correlated and provide valuable information for more robust background correction. Herein, we propose two new strategies to remove background for a set of related spectra collaboratively. Based on weighted penalized least squares, the new approaches will use the fused weights from multiple spectra or the weights from the average spectrum to estimate the background of each spectrum in the set. Background correction results from both simulated and real experimental data demonstrate that the proposed collaborative approaches outperform traditional algorithms which process spectra individually.

An Automated Baseline Correction Method Based on Iterative Morphological Operations

Raman spectra usually suffer from baseline drift caused by fluorescence or other reasons. Therefore, baseline correction is a necessary and crucial step that must be performed before subsequent processing and analysis of Raman spectra. An automated baseline correction method based on iterative morphological operations is proposed in this work. The method can adaptively determine the structuring element first and then gradually remove the spectral peaks during iteration to get an estimated baseline. Experiments on simulated data and real-world Raman data show that the proposed method is accurate, fast, and flexible for handling different kinds of baselines in various practical situations. The comparison of the proposed method with some state-of-the-art baseline correction methods demonstrates its advantages over the existing methods in terms of accuracy, adaptability, and flexibility. Although only Raman spectra are investigated in this paper, the proposed method is hopefully to be used for the baseline correction of other analytical instrumental signals, such as IR spectra and chromatograms.

Speeding up Raman spectral imaging by the three-dimensional low rank estimation method

Raman spectral imaging has been widely used as a very important analytical tool in various fields. For obtaining the high spectral signal-to-noise ratio Raman images, the long integration time is necessary, which is placing a limit on the application of Raman spectral imaging. We introduce a simple and feasible numerical method of the Three-dimensional Low Rank Estimation (3D-LRE), which can speed up the data acquisition process of the Raman spectral imaging. The spectral signal-to-noise ratio of the Raman images can be increased by over 75 times and the speed of the data acquisition can be improved by over 30 times. By combining with line-scan or multifocus-scan techniques, the Raman images can be obtained in a few seconds.

Autocorrelation Analysis Combined with a Wavelet Transform Method to Detect and Remove Cosmic Rays in a Single Raman Spectrum

Cosmic rays (CRs) occasionally affect charge-coupled device (CCD) detectors, introducing large spikes with very narrow bandwidth in the spectrum. These CR features can distort the chemical information expressed by the spectra. Consequently, we propose here an algorithm to identify and remove significant spikes in a single Raman spectrum. An autocorrelation analysis is first carried out to accentuate the CRs feature as outliers. Subsequently, with an adequate selection of the threshold, a discrete wavelet transform filter is used to identify CR spikes. Identified data points are then replaced by interpolated values using the weighted-average interpolation technique. This approach only modifies the data in a close vicinity of the CRs. Additionally, robust wavelet transform parameters are proposed (a desirable property for automation) after optimizing them with the application of the method in a great number of spectra. However, this algorithm, as well as all the single-spectrum analysis procedures, is limited to the cases in which CRs have much narrower bandwidth than the Raman bands. This might not be the case when low-resolution Raman instruments are used.

Raman imaging of drug delivery systems

This review article includes an introduction to the principals of Raman spectroscopy, an outline of the experimental systems used for Raman imaging and the associated important considerations and limitations of this method. Common spectral analysis methods are briefly described and examples of interesting published studies which utilised Raman imaging of pharmaceutical and biomedical devices are discussed, along with summary tables of the literature at this point in time.

Goldindec: A Novel Algorithm for Raman Spectrum Baseline Correction

Raman spectra have been widely used in biology, physics, and chemistry and have become an essential tool for the studies of macromolecules. Nevertheless, the raw Raman signal is often obscured by a broad background curve (or baseline) due to the intrinsic fluorescence of the organic molecules, which leads to unpredictable negative effects in quantitative analysis of Raman spectra. Therefore, it is essential to correct this baseline before analyzing raw Raman spectra. Polynomial fitting has proven to be the most convenient and simplest method and has high accuracy. In polynomial fitting, the cost function used and its parameters are crucial. This article proposes a novel iterative algorithm named Goldindec, freely available for noncommercial use as noted in text, with a new cost function that not only conquers the influence of great peaks but also solves the problem of low correction accuracy when there is a high peak number. Goldindec automatically generates parameters from the raw data rather than by empirical choice, as in previous methods. Comparisons with other algorithms on the benchmark data show that Goldindec has a higher accuracy and computational efficiency, and is hardly affected by great peaks, peak number, and wavenumber.

Recovery of Raman spectra with low signal-to-noise ratio using Wiener estimation

Raman spectroscopy is a powerful non-destructive technique for qualitatively and quantitatively characterizing materials. However, noise often obscures interesting Raman peaks due to the inherently weak Raman signal, especially in biological samples. In this study, we develop a method based on spectral reconstruction to recover Raman spectra with low signal-to-noise ratio (SNR). The synthesis of narrow-band measurements from low-SNR Raman spectra eliminates the effect of noise by integrating the Raman signal along the wavenumber dimension, which is followed by spectral reconstruction based on Wiener estimation to recover the Raman spectrum with high spectral resolution. Non-negative principal components based filters are used in the synthesis to ensure that most variance contained in the original Raman measurements are retained. A total of 25 agar phantoms and 20 bacteria samples were measured and data were used to validate our method. Four commonly used de-noising methods in Raman spectroscopy, i.e. Savitzky-Golay (SG) algorithm, finite impulse response (FIR) filtration, wavelet transform and factor analysis, were also evaluated on the same set of data in addition to the proposed method for comparison. The proposed method showed the superior accuracy in the recovery of Raman spectra from measurements with extremely low SNR, compared with the four commonly used de-noising methods.

Improving the detection sensitivity of chromatography by stochastic resonance

This review aims to provide readers with an overview of various methodologies and approaches used to improve sensitivity through stochastic resonance (SR) methods, with special emphasis on applications to improve the detectability of analytes in chromatographic signals.