A novel method to calculate the approximate derivative photoacoustic spectrum using continuous wavelet transform

Sparse decomposition enables adaptive and accurate Raman spectral denoising

Enhancing the quality of spectral denoising plays a vital role in Raman spectroscopy. Nevertheless, the intricate nature of the noise, coupled with the existence of impurity peaks, poses significant challenges to achieving high accuracy while accommodating various Raman spectral types. In this study, an innovative adaptive sparse decomposition denoising (ASDD) method is proposed for denoising Raman spectra. This approach features several innovations. Firstly, a dictionary comprising spectral feature peaks is established from the input spectra by applying a chemometric feature extraction method, which better aligns with the original data compared to traditional dictionaries. Secondly, a dynamic Raman spectral dictionary construction technique is introduced to swiftly adapt to new substances, employing a limited amount of additional Raman spectral data. Thirdly, the orthogonal matching pursuit algorithm is utilized to sparsely decompose the Raman spectra onto the constructed dictionaries, effectively eliminating various random and background noises in the Raman spectra. Empirical results confirm that ASDD enhances the accuracy and robustness of denoising Raman spectra. Significantly, ASDD surpasses existing algorithms in processing Raman spectra of pesticide.

Revealing the interactions of water with cryoprotectant and protein by near-infrared spectroscopy

Taking formamide (FA) as a model compound of protein, the water structure in the ternary mixtures of dimethyl sulfoxide (DMSO)-water-FA was studied by near-infrared (NIR) spectroscopy. The interaction of DMSO and water, and the effect of FA on the interaction, were analyzed with the help of chemometric methods. Continuous wavelet transform (CWT) was used to enhance the resolution of the spectra. A peak at 6437 cm^-1 depicting the interaction of DMSO and water through hydrogen bonding (SO…HO) was observed in the transformed spectra. When FA exists in the mixture, the intensity of the peak decreases with the increase of formamide content, showing that FA may replace the water to form the hydrogen bond of SO and HN. In addition, temperature-dependent NIR spectroscopy was used to analyze the effect of the three components on the spectral variation with temperature. Analyzing the spectral data by alternating trilinear decomposition (ATLD) and multiple linear regression, two varying spectral features were obtained that are related to water and DMSO, but no spectral feature was found that significantly varies with the content of FA. The result implies that DMSO is still the key component to prevent the water from icing, although FA may reduce slightly the anti-freezing effect.

Correcting frequency and phase offsets in MRS data using robust spectral registration

An algorithm for retrospective correction of frequency and phase offsets in MRS data is presented. The algorithm, termed robust spectral registration (rSR), contains a set of subroutines designed to robustly align individual transients in a given dataset even in cases of significant frequency and phase offsets or unstable lipid contamination and residual water signals. Data acquired by complex multiplexed editing approaches with distinct subspectral profiles are also accurately aligned. Automated removal of unstable lipid contamination and residual water signals is applied first, when needed. Frequency and phase offsets are corrected in the time domain by aligning each transient to a weighted average reference in a statistically optimal order using nonlinear least-squares optimization. The alignment of subspectra in edited datasets is performed using an approach that specifically targets subtraction artifacts in the frequency domain. Weighted averaging is then used for signal averaging to down-weight poorer-quality transients. Algorithm performance was assessed on one simulated and 67 in vivo pediatric GABA-/GSH-edited HERMES datasets and compared with the performance of a multistep correction method previously developed for aligning HERMES data. The performance of the novel approach was quantitatively assessed by comparing the estimated frequency/phase offsets against the known values for the simulated dataset or by examining the presence of subtraction artifacts in the in vivo data. Spectral quality was improved following robust alignment, especially in cases of significant spectral distortion. rSR reduced more subtraction artifacts than the multistep method in 64% of the GABA difference spectra and 75% of the GSH difference spectra. rSR overcomes the major challenges of frequency and phase correction.

Three-level simultaneous component analysis for analyzing the near-infrared spectra of aqueous solutions under multiple perturbations

Quantitative analysis under various perturbations is a difficult problem because the analytical signal changes with different factors. In this work, three-level simultaneous component analysis (3-MSCA) was used for analyzing the near-infrared (NIR) spectra of aqueous solutions under different perturbations. The spectral data of aqueous proline solutions at different pH, concentration and temperature were measured, and a three-level model was built to describe the effects of the three perturbations on the spectra, respectively. The first level model describes the change of the spectra with pH, from which significant aggregation of proline was observed around the isoelectric point. The second and third level model show the spectral change with concentration and temperature, respectively, and the spectral feature has a very good linear relationship with the corresponding influencing factors. Therefore, the pH and concentration scores can be used as the calibration curve for quantitative analysis of the pH and the content of proline, and the temperature scores can be used to predict the temperature of the solutions. In addition, the structural change of water molecules under different conditions is obtained from the loadings. A decline of the bulk water was found with the increase of concentration, implying an ascending trend of the bonded water due to the interaction of proline and water. The dissociation of water clusters with the increase of temperature is also displayed.

Interaction between tau and water during the induced aggregation revealed by near-infrared spectroscopy

Near-infrared (NIR) spectra are sensitive to the variation of water structure. In this work, NIR spectroscopy was used to investigate the variation of hydration water during the aggregation of R2/wt induced by heparin. The osmolytes, urea and trehalose, were used to slow down and speed up the aggregation. The spectra of R2/wt aqueous solution obtained by NIR spectroscopy at 37 °C were adopted to analyze the structure of water during the aggregation. The spectral features of different water species were observed by principal component analysis (PCA) from the resolution enhanced NIR spectra. The existence of the water molecules with one and two hydrogen bonds around the NH and CH groups of R2/wt, respectively, was suggested, and the variation of the hydrogen-bonded water was found to be an indicator to monitor the process of aggregation. Then, the variation of the water species during the aggregation was analyzed by two-dimensional correlation spectroscopy. The water hydrogen bonded with NH group was found to change earlier than the water around the hydrophobic groups. The results suggest that β-sheet forms though the hydrogen bonds of amide groups in the early stage of the aggregation, and the destruction of the hydrogen bond network of the water around the side chains maybe the main reason for the formation of the ordered amyloid fibers.

Understanding the complexity of the structures in alcohol solutions by temperature-dependent near-infrared spectroscopy

For understanding the structures and the hydrogen bonding in alcohol solutions, the changes of the structures and hydrogen bonding with temperature were studied by temperature-dependent near-infrared (NIR) spectroscopy. The spectral features of eight alcohol species including the monomer, dimer and linear or cyclic aggregates (trimer, tetramer and polymer) were found from the resolution-enhanced spectra calculated by continuous wavelet transform. The changes of the eight species with concentration and temperature were analyzed using the intensity variation of the corresponding spectral features and two-dimensional correlation NIR spectroscopy. The aggregates were found to form at a very low concentration and the stability of the seven aggregates with temperature was found in an order of cyclic tetramer > linear polymer > linear tetramer > cyclic trimer > linear trimer > cyclic polymer > dimer. Furthermore, the formation of the aggregates was found to be affected by the chain length. The increase of the chain length is beneficial for the formation of cyclic tetramer and polymer due to the hydrophobic effect, but is an adverse effect for the formation of linear polymer.

High order derivative to investigate the complexity of the near infrared spectra of aqueous solutions

Derivative calculation is a powerful method for resolution enhancement in spectral analysis. A high order derivative method based on continuous wavelet transform (CWT) is discussed in the analysis of near infrared (NIR) spectra. The results for a simulated spectrum obtained from conventional numerical differentiation (NM), Fourier transform (FT), Savitzky-Golay (SG) and CWT method were compared. CWT method was found to be as efficient as FT and SG, but easier for high order derivative computation, and the fourth order derivative was proved to be a good choice for resolution enhancement as well as reduction of noise and sidelobe effects. For the NIR spectra of water-ethanol mixtures, the complexity of the spectra can be observed from the fourth derivative, including the spectral features of OH and CH with various intermolecular interactions. Fitting the derivative spectra of the mixtures by those of pure water and ethanol, the obtained coefficients for ethanol show a linear relation with the content but that for water exhibit a non-linear relation, which reveals the influence of ethanol on water structure in the mixture. Furthermore, the information of the water-ethanol clusters was found in the residual spectra after the fitting. Therefore, high order derivative can be an efficient way to improve the resolution of NIR spectra for understanding the interactions in aqueous solutions.

Understanding the role of water in the aggregation of poly(N,N-dimethylaminoethyl methacrylate) in aqueous solution using temperature-dependent near-infrared spectroscopy

For understanding the role of water in the aggregation of polymers, the variation of water structures with the structural change of polymers in the process of aggregation was studied by temperature-dependent near-infrared (NIR) spectroscopy. The NIR spectra of the aqueous poly(N,N-dimethylaminoethyl methacrylate) (PDMAEMA) solutions of different concentrations were measured at different temperatures. The spectral changes of the polymer and water with temperature were analyzed by N-way principal component analysis (NPCA). It was found that, at low concentration, the chains of the polymer tend to form a loose hydrophobic structure below 36 °C and then aggregate into a micelle at a lower critical solution temperature (LCST) of around 39 °C. In the process of the aggregation, the water species with two hydrogen bonds (S2) increases gradually before 36 °C and then a sudden decrease occurs after that temperature. The results clearly indicate that water species S2 plays an important role in the formation of the intermediate, i.e., the loose hydrophobic structure of the polymer chains linked by the two hydrogen bonds of S2 water. When the temperature increases, the dissociation of the hydrogen bonds enables the intermediate to be destroyed to form a micelle structure. For the high concentration solution, however, the spectral information of S2 was not found in the aggregation, suggesting direct formation of the micelle from the dehydrated chains.

A Novel Pre-Processing Algorithm Based on the Wavelet Transform for Raman Spectrum

Noise and fluorescent background are two major problems for acquiring Raman spectra from samples, which blur Raman spectra and make Raman detection or imaging difficult. In this paper, a novel algorithm based on wavelet transform that contains denoising and baseline correction is presented to automatically extract Raman signals. For the denoising section, the improved conventional-scale correlation denoising method is proposed. The baseline correction section, which is performed after denoising, basically consists of five aspects: (1) detection of the peak position; (2) approximate second derivative calculation based on continuous wavelet transform is performed using the Haar wavelet function to find peaks and background areas; (3) the threshold is estimated from the peak intensive area for identification of peaks; (4) correction of endpoints, spectral peaks, and peak position; and (5) determine the endpoints of the peak after subtracting the background. We tested this algorithm for simulated and experimental Raman spectra, and a satisfactory denoising effect and a good capability to correct background are observed. It is noteworthy that this algorithm requires few human interventions, which enables automatic denoising and background removal.

Understanding the Interaction Between Oligopeptide and Water in Aqueous Solution Using Temperature-Dependent Near-Infrared Spectroscopy

Investigating the interaction between oligopeptide and water is essential for understanding the structure, dynamics and function of proteins. Temperature-dependent near-infrared (NIR) spectroscopy and independent component analysis (ICA) were employed to study the interaction between oligopeptide and water in aqueous solution. The NIR spectra of two homo-oligopeptides, penta-aspartic acid (D₅) and penta-lysine (K₅), in aqueous solution of different concentration were measured at different temperature (30-90 ℃). Independent component analysis was performed to extract the spectral information that changes with temperature. The independent components (ICs) representing the spectral information of NH and CH₂ groups were obtained. Compared with D₅, the two groups in K₅ change significantly at higher temperature. The result may suggest that K₅ has stronger interaction with water than D₅. Moreover, three ICs that contain the spectral information of the water species with no (S₀), one (S₁), and two (S₂) hydrogen-bonds were obtained. It was shown that the spectral intensity of S₀ and S₁ increases while that of S₂ decreases with the temperature, and the changes of oligopeptide solutions are weaker than those of pure water. The results indicate that water structure is sensitive to temperature and the oligopeptide in aqueous solution improves the thermal stability of the water species. When oligopeptide is added, the spectral intensity of S₀ and S₂ decreases and that of S₁ increases for D₅ solution, but the intensity of all the three species decreases for K₅ solution. Furthermore, the concentration effect of K₅ was found to be stronger than D₅. The result may reveal that D₅ combines with water molecule through forming one hydrogen bond but K₅ interacts with water through a different way.

Understanding the function of water during the gelation of globular proteins by temperature-dependent near infrared spectroscopy

Water plays an indispensable role in the gelation of proteins, but its function still remains unclear. In this work, the variation of water species with the structural changes of globular proteins was investigated using temperature-dependent near infrared (NIR) spectroscopy. Ovalbumin (OVA) was used as a model protein, which forms a gel-like structure as the temperature increases through three phases, i.e., phase I (native), phase II (molten globule state), and phase III (gel state). The structural change and the content variation of different water species in the three phases of gelation were analyzed by two-dimensional correlation NIR spectroscopy and Gaussian fitting. A decrease in the water species with two hydrogen bonds (S2) was found and the change follows the same phases as OVA. In the first two phases, the change occurs after those of other water species but in the third phase, the change is faster than that of free water species. The result indicates that in the native and molten globule states, S2 is located in the hydration shell of OVA to maintain the stability of the protein structure, and then in the gel state, high temperature weakens the hydrogen bonding of S2 and leads to the destruction of the hydration shell, making OVA clusters form a gel structure.

Multiscale peak alignment for chromatographic datasets

Chromatography has been extensively applied in many fields, such as metabolomics and quality control of herbal medicines. Preprocessing, especially peak alignment, is a time-consuming task prior to the extraction of useful information from the datasets by chemometrics and statistics. To accurately and rapidly align shift peaks among one-dimensional chromatograms, multiscale peak alignment (MSPA) is presented in this research. Peaks of each chromatogram were detected based on continuous wavelet transform (CWT) and aligned against a reference chromatogram from large to small scale gradually, and the aligning procedure is accelerated by fast Fourier transform cross correlation. The presented method was compared with two widely used alignment methods on chromatographic dataset, which demonstrates that MSPA can preserve the shapes of peaks and has an excellent speed during alignment. Furthermore, MSPA method is robust and not sensitive to noise and baseline. MSPA was implemented and is available at http://code.google.com/p/mspa.

Simultaneous spectrophotometric determination of cyproterone acetate and ethinyl estradiol in tablets using continuous wavelet and derivative transform

In this study a zero crossing technique based on continuous wavelet transform (CWT) as well as classical derivative spectrophotometry (CDS) is presented for simultaneous determination of cyproterone acetate and ethinyl estradiol in binary mixtures and commercial dosage of drug, without using prior chemical pre-treatment. Absorption spectra were recorded in the wavelength range 200-400 nm. Absorbance data were subjected to various mother wavelets from continuous wavelet transform family to find the optimum point of the wavelet signal processing (Matlab 7.5) gaus 15 and morl wavelet functions with scaling factor, a=70 and 3rd derivative with Deltalambda=10 nm, were selected. Optimum value of scaling factor was chosen to obtain an appropriate calibration for each method. The validation of proposed methods was investigated by several synthetic mixtures and obtained results were successfully compared among each other. Mean recovery values were found between 96.93% and 101.7% for CWT and 95.55% and 104.22% for DS, respectively for the determination of cyproterone acetate and ethinyl estradiol in synthetic mixtures. The developed methods are rapid, precise and easy to apply for the analysis of overlapping signals of the components in the mixtures. Obtained results from the CWT were compared to those yielded by CDS which were in good agreement and therefore led to a successful determination.

Characterization of a derivative photoacoustic spectrometer

A design of derivative photoacoustic spectrometer is presented in this article. It mainly includes a wavelength-intensity splitter and a complementary chopper. In our design, a dual wavelength derivative method is introduced to implement a derivative operation. Through the wavelength-intensity splitter, two beams are obtained and then complementarily modulated by the complementary chopper to satisfy the first derivative requirements as well as to achieve the differential of photoacoustic signals. As examples, the first derivative photoacoustic spectra of He-Ne laser and xenon lamp are also presented in this article. The results show that the first derivative photoacoustic spectrum can provide a superior fine spectral structure and spectral resolution compared to the photoacoustic absorption spectrum.

An adaptive strategy for selecting representative calibration samples in the continuous wavelet domain for near-infrared spectral analysis

Sample selection is often used to improve the cost-effectiveness of near-infrared (NIR) spectral analysis. When raw NIR spectra are used, however, it is not easy to select appropriate samples, because of background interference and noise. In this paper, a novel adaptive strategy based on selection of representative NIR spectra in the continuous wavelet transform (CWT) domain is described. After pretreatment with the CWT, an extension of the Kennard-Stone (EKS) algorithm was used to adaptively select the most representative NIR spectra, which were then submitted to expensive chemical measurement and multivariate calibration. With the samples selected, a PLS model was finally built for prediction. It is of great interest to find that selection of representative samples in the CWT domain, rather than raw spectra, not only effectively eliminates background interference and noise but also further reduces the number of samples required for a good calibration, resulting in a high-quality regression model that is similar to the model obtained by use of all the samples. The results indicate that the proposed method can effectively enhance the cost-effectiveness of NIR spectral analysis. The strategy proposed here can also be applied to different analytical data for multivariate calibration.

A new general-purpose fully automatic baseline-correction procedure for 1D and 2D NMR data

A new procedure for automatic baseline correction of NMR data sets is presented. It is based on an improved automatic recognition of signal-free regions that uses a Continuous Wavelet transform derivative calculation, followed by a baseline modelling procedure based on the Whittaker smoother algorithm. The method has been proven to automatically flatten 1D and 2D NMR spectra with large baseline distortions arising from different sources, is tolerant to low signal-to-noise ratio spectra, and to signals of varying widths in a single spectrum. Even though this procedure has so far only been applied to NMR spectra, we believe it to also be applicable to other spectroscopies having relatively narrow peaks (e.g., mass spectrometry), and potentially to those with broad peaks (e.g., near infrared or ultraviolet).

Resolution enhancement of composite spectra using wavelet-based derivative spectrometry

An approach based on the using of the continuous wavelet transform (CWT) in derivative spectrometry (DS) is considered. Within the framework of the approach we develop a numerical differentiation algorithm with continuous wavelets for improving resolution of composite spectra. The wavelet-based derivative spectrometry (WDS) method results in best contrast in differential curves compared to the conventional derivative spectrometry method. A main advantage is that, as opposed to DS, WDS gives stable estimations of derivative in the wavelet domain without using the regularization. A wavelet shape and the information redundancy are of the greatest importance when the continuous wavelet transform is used. As an appropriate wavelet we offer to utilize the nth derivative of a component with a priori known shape. The energy distribution into scales allows one to determine a unique wavelet projection and in that way to avoid the information redundancy. A comparative study of WDS and DS with the statistical regularization method (SRM) is made; in particular, limits of applicability of these are given. Examples of the application of both DS and WDS for improving resolution of synthetic composite bands and real-world composite ones coming from molecular spectroscopy are given.

A new hybrid strategy for constructing a robust calibration model for near-infrared spectral analysis

A new hybrid algorithm is proposed for construction of a high-quality calibration model for near-infrared (NIR) spectra that is robust against both spectral interference (including background and noise) and multiple outliers. The algorithm is a combination of continuous wavelet transform (CWT) and a modified iterative reweighted PLS (mIRPLS) procedure. In the proposed algorithm the spectral interference is filtered by CWT at the first stage then mIRPLS is proposed to detect the multiple outliers in the CWT domain. Compared with the original IRPLS method, mIRPLS does not need to adjust variable parameters to achieve optimum calibration results, which makes it very convenient to perform in practice. The final PLS model is constructed robustly because both the spectral interference and multiple outliers are eliminated. In order to validate the effectiveness and universality of the algorithm, it was applied to two different sets of NIR spectra. The results indicate that the proposed strategy can greatly enhance the robustness and predictive ability of NIR spectral analysis.

Signals ratio method combined with wavelet transform: application to resolution of overlapped electrochemical signals

A signals ratio method combined with wavelet transform was proposed for the resolution of a weak voltammetric signal overlapped by other components. The signals ratio method usually suffers from interference from noise and baseline contained in the original signals because these factors cause distortion of the signals ratio. The multiresolution capability of the wavelet transform method was exploited here to simultaneously remove or reduce the noise and background. As a result, a deformation-free signals ratio with good signal-to-noise ratio (SNR) was obtained even for very noisy signals. The properties of the proposed method were compared to other resolution methods. It was demonstrated that the combined signals ratio wavelet transform method was particularly applicable to resolve a minor component in the presence of large amount of other components, suggesting that it can provide improved detection limits and quantified results for minor components. The method was employed for the voltammetric determination of residual chlorine in the presence of N,N-diethyl-p-phenylenediamine (DPD).

Continuous Wavelet Transform Applied to Removing the Fluctuating Background in Near-Infrared Spectra

A novel method based on continuous wavelet transform (CWT) was proposed as a preprocessing tool for the near-infrared (NIR) spectra. Due to the property of the vanishing moments of the wavelet, the fluctuating background of the NIR spectra can be successfully removed through convolution of the spectra with an appropriate wavelet function. The vanishing moments of a wavelet and the scale parameter are two key factors that govern the result of the background elimination. The result of its application to both the simulated spectra and the NIR spectra of tobacco samples demonstrates that CWT is a competitive tool for removing fluctuating background in spectra.

A zero-crossing technique for the multidetermination of thiamine HCl and pyridoxine HCl in their mixture by using one-dimensional wavelet transform

A new zero-crossing technique based on one-dimensional wavelet transform (WT) was developed and applied on a commercial vitamin product and binary mixtures containing thiamine HCl and pyridoxine HCl in the presence of the interference of the analysed signals. We selected from the data of the UV-Vis absorption spectra a signal consisting of 1150 points corresponding to the concentration range 8-32 mg/ml for both vitamins and we subjected it to one-dimensional continuous WT Mexican (MEXICAN) and Meyer (MEYER). Since the peaks of the transformed signals were bigger than original ones a zero crossing technique was applied to obtain the regression equations. The validity of Beer-Lambert law was assumed for the transformed signals. An appropriate scale setting was choosing to obtain an alternative calibration for each method. The basic concepts about wavelet method were briefly explained and MATLAB 6.5 software was used for one-dimensional wavelet analysis. The obtained results were successfully compared among each other and with those obtained by other literature methods. The developed method is rapid, easy to apply, not expensive and suitable for analysing of the overlapping signals of compounds in their mixtures without any chemical pre-treatment.