Skip to main content

Advertisement

SpringerLink
Log in

Recursive Wavelet Peak Detection of Analytical Signals

  • Original
  • Published:
Chromatographia Aims and scope Submit manuscript

Abstract

A novel algorithm, entitled recursive wavelet peak detection (RWPD), is proposed to detect both normal and overlapped peaks in analytical signals. Recursive peak detection is based on continuous wavelet transforms (CWTs), which can be used to obtain initial peak positions even for overlapped peaks. Genetic algorithm (GA) and Gaussian fitting are used to refine peak parameters (peak positions, widths, and heights). Finally, area of peaks can be calculated by numeric integration. Simulated and ultrahigh performance liquid chromatographic ion trap time-of-flight mass spectrometry (UPLC-IT-TOF-MS) data sets have been analyzed by RWPD, MassSpecWavelet, and peakfit package by Tom O’Haver. Results show that RWPD can obtain more accurate positions and smaller relative fitting errors than MassSpecWavelet and peakfit, especially in overlapped peaks. RWPD is a convenient tool for peak detection and deconvolution of overlapped peaks, and it has been developed in R programming language and is available at https://github.com/zmzhang/RWPD.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Kronewitter SR, Slysz GW, Marginean I, Hagler CD, LaMarche BL, Zhao R, Harris MY, Monroe ME, Polyukh CA, Crowell KL, Fillmore TL, Carlson TS, Camp DG 2nd, Moore RJ, Payne SH, Anderson GA, Smith RD (2014) GlyQ-IQ: glycomics quintavariate-informed quantification with high-performance computing and GlycoGrid 4D visualization. Anal Chem 86:6268–6276

    Article  CAS  Google Scholar 

  2. Lopatka M, Vivo-Truyols G, Sjerps MJ (2014) Probabilistic peak detection for first-order chromatographic data. Anal Chim Acta 817:9–16

    Article  CAS  Google Scholar 

  3. Vivo-Truyols G, Torres-Lapasió JR, Van Nederkassel AM, Heyden YV, Massart DL (2005) Automatic program for peak detection and deconvolution of multi-overlapped chromatographic signals Part I: peak detection. J Chromatogr A 1096:133–145

    Article  CAS  Google Scholar 

  4. Vivo-Truyols G, Torres-Lapasió JR, Van Nederkassel AM, Heyden YV, Massart DL (2005) Automatic program for peak detection and deconvolution of multi-overlapped chromatographic signals Part II: peak model and deconvolution algorithms. J Chromatogr A 1096:146–155

    Article  CAS  Google Scholar 

  5. Tom OH (2015) A pragmatic introduction to signal processing with applications in scientific measurement. http://terpconnect.umd.edu/~toh/spectrum/index.html. Accessed 12 Mar 2015

  6. Du P, Kibbe WA, Lin SM (2006) Improved peak detection in mass spectrum by incorporating continuous wavelet transform-based pattern matching. Bioinformatics 22:2059–2065

    Article  CAS  Google Scholar 

  7. Zhang Z-M, Chen S, Liang Y-Z, Liu Z-X, Zhang Q-M, Ding L-X, Ye F, Zhou H (2009) An intelligent background-correction algorithm for highly fluorescent samples in Raman spectroscopy. J Raman Spectrosc 41:659–669

    Article  Google Scholar 

  8. Zhang Z-M, Chen S, Liang Y-Z (2011) Peak alignment using wavelet pattern matching and differential evolution. Talanta 83:1108–1117

    Article  CAS  Google Scholar 

  9. Zhang Z-M, Liang Y-Z, Lu H-M, Tan B-B, Xu X-N, Ferro M (2012) Multiscale peak alignment for chromatographic datasets. J Chromatogr A 1223:93–106

    Article  CAS  Google Scholar 

  10. Zheng Y-B, Zhang Z-M, Liang Y-Z, Zhan D-J, Huang J-H, Yun Y-H, Xie H-L (2013) Application of fast Fourier transform cross-correlation and mass spectrometry data for accurate alignment of chromatograms. J Chromatogr A 1286:175–182

    Article  CAS  Google Scholar 

  11. Zhang Z-M, Tong X, Peng Y, Ma P, Zhang M-J, Lu H-M, Chen X-Q, Liang Y-Z (2015) Multiscale peak detection in wavelet space. Analyst 140:7955–7964

    Article  CAS  Google Scholar 

  12. Coombes KR, Tsavachidis S, Morris JS, Baggerly KA, Hung M-C, Kuerer HM (2005) Improved peak detection and quantification of mass spectrometry data acquired from surface-enhanced laser desorption and ionization by denoising spectra with the undecimated discrete wavelet transform. Proteomics 5:4107–4117

    Article  CAS  Google Scholar 

  13. Mantini D, Petrucci F, Pieragostino D, Del Boccio P, Di Nicola M, Di Ilio C, Federici G, Sacchetta P, Comani S, Urbani A (2007) LIMPIC: a computational method for the separation of protein MALDI-TOF-MS signals from noise. BMC Bioinformatics 8:101

    Article  Google Scholar 

  14. Yasui Y, Pepe M, Thompson ML, Adam B-L, Qu Y, Potter J, Winget M, Thornquist M, Feng Z (2003) A data-analytic strategy for protein biomarker discovery: profiling of high-dimensional proteomic data for cancer detection. Biostatistics 4:449–463

    Article  Google Scholar 

  15. Li X, Gentleman R, Lu X, Shi Q, Iglehart J, Harris L, Miron A (2005) SELDI-TOF mass spectrometry protein data. In: Gentleman R, Carey VJ, Huber W, Irizarry RA, Dudoit S (eds) Bioinformatics and computational biology solutions using R and bioconductor. Springer, China

  16. Yang C, He Z, Yu W (2009) Comparison of public peak detection algorithms for MALDI mass spectrometry data analysis. BMC Bioinformatics 10:4–17

    Article  Google Scholar 

  17. Caballero RD, Garcıa-Alvarez-Coque MC, Baeza-Baeza JJ (2002) Parabolic-Lorentzian modified Gaussian model for describing and deconvolving chromatographic peaks. J Chromatogr A 954:59–76

    Article  CAS  Google Scholar 

  18. Buys TS, De Clerk K (1972) Bi-Gaussian fitting of skewed peaks. Anal Chem 69:3822–3831

    Google Scholar 

  19. Nikitas P, Pappa-Louisi A, Papageorgiou A (2001) On the equations describing chromatographic peaks and the problem of the deconvolution of overlapped peaks. J Chromatogr A 912:13–29

    Article  CAS  Google Scholar 

  20. Li J-W (2002) Comparison of the capability of peak functions in describing real chromatographic peaks. J Chromatogr A 952:63–70

    Article  CAS  Google Scholar 

  21. Marco VBD, Bombi GG (2001) Mathematical functions for the representation of chromatographic peaks. J Chromatogr A 931:1–30

    Article  Google Scholar 

  22. Zeng Z-D, Chin S-T, Hugel HM, Marriott PJ (2011) Simultaneous deconvolution and re-construction of primary and secondary overlapping peak clusters in comprehensive two-dimensional gas chromatography. J Chromatogr A 1218(16):2301–2310

    Article  CAS  Google Scholar 

  23. Zhang Z-M, Chen S, Liang Y-Z (2010) Baseline correction using adaptive iteratively reweighted penalized least squares. Analyst 135:1138–1146

    Article  CAS  Google Scholar 

  24. Galiana-Merino JJ, Pla C, Fernandez-Cortes A, Cuezva S, Ortiz J, Benavente D (2014) EnvironmentalWaveletTool: continuous and discrete wavelet analysis and filtering for environmental time series. Comput Phys Commun 185:2758–2770

    Article  CAS  Google Scholar 

  25. Liu Y, Cai W-S, Shao X-G (2013) Intelligent background correction using an adaptive lifting wavelet. Chemometr Intell Lab 125:11–17

    Article  CAS  Google Scholar 

  26. Shao XG, Cai WS, Sun PY (1998) Determination of the component number in overlapping multicomponent chromatogram using wavelet transform. Chemometr Intell Lab 43:147–155

    Article  CAS  Google Scholar 

  27. Shao XG, Leung AK-M, Chau FT (2003) Wavelet: a new trend in chemistry. Acc Chem Res 36:276–283

    Article  CAS  Google Scholar 

  28. Shao XG, Gu H, Wu JH, Shi YY (2000) Resolution of the NMR spectrum using wavelet transform. Appl Spectrosc 54:731–738

    Article  CAS  Google Scholar 

  29. Shao XG, Cai WS, Sun PY, Zhang MS, Zhao GW (1997) Quantitative determination of the components in overlapping chromatographic peaks using wavelet transform. Anal Chem 69:1722–1725

    Article  CAS  Google Scholar 

  30. Jiao L, Gao S, Zhang F, Li H (2008) Quantification of components in overlapping peaks from capillary electrophoresis by using continues wavelet transform method. Talanta 75:1061–1067

    Article  CAS  Google Scholar 

  31. Mohammadpour K, Sohrabi MR, Jourabchi A (2010) Continuous wavelet and derivative transform applied to the overlapping spectra for the quantitative spectrophotometric multi-resolution of triamterene and hydrochlorothiazide in triamterene-H tablets. Talanta 81:1821–1825

    Article  CAS  Google Scholar 

  32. Nikitas P, Pappa-Louisi A, Papageorgiou A (2007) Simple algorithms for fitting and optimisation for multilinear gradient elution in reversed-phase liquid chromatography. J Chromatogr A 1157:178–186

    Article  CAS  Google Scholar 

  33. Bolanča T, Ukić Š, Novak M, Rogošić M (2014) Computer assisted method development in liquid chromatography. Croat Chem Acta 87:111–122

    Article  Google Scholar 

  34. Zhang XT, Zhu HY, Zhang HB (1998) Robust grey model based on genetic algorithms and its application to prediction for chromatographic retention. Chemometr Intell Lab 44:197–203

    Article  CAS  Google Scholar 

  35. Shao XG, Chen ZH, Lin XQ (2000) Resolution of multicomponent overlapping chromatogram using an immune algorithm and genetic algorithm. Chemometr Intell Lab 50:91–99

    Article  CAS  Google Scholar 

  36. Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press, Cambridge

    Google Scholar 

  37. Larsen FH, van den Berg F, Engelsen SB (2006) An exploratory chemometric study of1H NMR spectra of table wines. J Chemometr 20:198–208

    Article  CAS  Google Scholar 

  38. Garcia-Talavera M, Ulicny B (2003) A genetic algorithm approach for multiplet deconvolution in γ-ray spectra. Nucl Instrum Meth Phys Res A 512:585–594

    Article  CAS  Google Scholar 

  39. Lovedy Singh L, Gartia RK (2014) Glow-curve deconvolution of thermoluminescence curves in the simplified OTOR equation using the hybrid genetic algorithm. Nucl Instrum Meth B 319:39–43

    Article  CAS  Google Scholar 

  40. Li Z, Zhan DJ, Wang JJ, Huang J, Xu QS, Zhang ZM, Zheng YB, Liang YZ, Wang H (2013) Morphological weighted penalized least squares for background correction. Analyst 138:4483–4492

    Article  CAS  Google Scholar 

  41. Liu XB, Zhang ZM, Sousa PFM, Chen C, Ouyang ML, Wei YC, Liang YZ, Chen Y, Zhang CP (2014) Selective iteratively reweighted quantile regression for baseline correction. Anal Bioanal Chem 406:1985–1998

    Article  CAS  Google Scholar 

  42. Liu XB, Zhang ZM, Liang YZ, Sousa PFM, Yun YH, Yu L (2014) Baseline correction of high resolution spectral profile data based on exponential smoothing. Chemometr Intell Lab 139:97–108

    Article  CAS  Google Scholar 

  43. Brennan RJ, Schiestl RH (1997) Diaminotoluenes induce intrachromosomal recombination and free radicals in Saccharomyces cerevisiae. Mutat Res-Fund Mol M 381:251–258

    Article  CAS  Google Scholar 

  44. Nakayama K, Kawano Y, Kawakami Y, Moriwaki N, Sekijima M, Otsuka M, Yakabe Y, Miyaura H, Saito K, Sumida K, Shirai T (2006) Differences in gene expression profiles in the liver between carcinogenic and non-carcinogenic isomers of compounds given to rats in a 28-day repeat-dose toxicity study. Toxicol Appl Pharmacol 217:299–307

    Article  CAS  Google Scholar 

  45. Toyoda-Hokaiwado N, Inoue T, Masumura K, Hayashi H, Kawamura Y, Kurata Y, Takamune M, Yamada M, Sanada H, Umemura T, Nishikawa A, Nohmi T (2010) Integration of in vivo genotoxicity and short-term carcinogenicity assays using F344 gpt delta transgenic rats: in vivo mutagenicity of 2,4-diaminotoluene and 2,6-diaminotoluene structural isomers. Toxicol Sci 114:71–78

    Article  CAS  Google Scholar 

  46. Dong LL, Shion H, Davis RG, Terry-Penak B, Castro-Perez J, Van Breemen RB (2010) Collision Cross-Section Determination and Tandem Mass Spectrometric Analysis of Isomeric Carotenoids Using Electrospray Ion Mobility Time-of-Flight Mass Spectrometry. Anal Chem 82:9014–9021

    Article  CAS  Google Scholar 

  47. Smith CA Saghatelian et al. (2004) FAAH knockout LC/MS data. http://bioconductor.org/packages/devel/data/experiment/manuals/faahKO/man/faahKO.pdf Accessed 31 July 2012

  48. Saghatelian A, Trauger SA, Want EJ, Hawkins EG, Siuzdak G, Cravatt BF (2004) Assignment of Endogenous Substrates to Enzymes by Global Metabolite Profiling. Biochemistry 43:14332–14339

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This study was supported by the National Nature Foundation Committee of People’s Republic of China (Grants No. 21275164, Grants No. 21375151 and Grants No. 21305163), Hunan Provincial Natural Science Foundation of China (Grants No. 14JJ3031), National Instrumentation Program of China (No. 2011YQ03012407) and China Postdoctoral Science Foundation (No. 2014M552146). The studies meet with the approval of the university’s review board. We are grateful to all employees of this institute for their encouragement and support of this research.

Author information

Authors and Affiliations

  1. Institute of Chemometrics and Intelligent Instruments, College of Chemistry and Chemical Engineering, Central South University, Changsha, 410083, People’s Republic of China

    Xia Tong, Zhimin Zhang, Fanjuan Zeng, Chunyan Fu, Pan Ma, Ying Peng, Hongmei Lu & Yizeng Liang

Authors
  1. Xia Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhimin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fanjuan Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chunyan Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Pan Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ying Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Hongmei Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Yizeng Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhimin Zhang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animal performed by any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tong, X., Zhang, Z., Zeng, F. et al. Recursive Wavelet Peak Detection of Analytical Signals. Chromatographia 79, 1247–1255 (2016). https://doi.org/10.1007/s10337-016-3155-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10337-016-3155-4

Keywords

Search

Navigation