WaveletQuant, an improved quantification software based on wavelet signal threshold denoising for labeled quantitative proteomic analysis
 Fan Mo†^{1},
 Qun Mo†^{2},
 Yuanyuan Chen^{1},
 David R Goodlett^{3},
 Leroy Hood^{4},
 Gilbert S Omenn^{5},
 Song Li^{2}Email author and
 Biaoyang Lin^{1, 6, 7}Email author
DOI: 10.1186/1471210511219
© Mo et al; licensee BioMed Central Ltd. 2010
Received: 7 August 2009
Accepted: 29 April 2010
Published: 29 April 2010
Abstract
Background
Quantitative proteomics technologies have been developed to comprehensively identify and quantify proteins in two or more complex samples. Quantitative proteomics based on differential stable isotope labeling is one of the proteomics quantification technologies. Mass spectrometric data generated for peptide quantification are often noisy, and peak detection and definition require various smoothing filters to remove noise in order to achieve accurate peptide quantification. Many traditional smoothing filters, such as the moving average filter, SavitzkyGolay filter and Gaussian filter, have been used to reduce noise in MS peaks. However, limitations of these filtering approaches often result in inaccurate peptide quantification. Here we present the WaveletQuant program, based on wavelet theory, for better or alternative MSbased proteomic quantification.
Results
We developed a novel discrete wavelet transform (DWT) and a 'Spatial Adaptive Algorithm' to remove noise and to identify true peaks. We programmed and compiled WaveletQuant using Visual C++ 2005 Express Edition. We then incorporated the WaveletQuant program in the TransProteomic Pipeline (TPP), a commonly used open source proteomics analysis pipeline.
Conclusions
We showed that WaveletQuant was able to quantify more proteins and to quantify them more accurately than the ASAPRatio, a program that performs quantification in the TPP pipeline, first using known mixed ratios of yeast extracts and then using a data set from ovarian cancer cell lysates. The program and its documentation can be downloaded from our website at http://systemsbiozju.org/data/WaveletQuant.
Background
Quantitative proteomics technologies have been developed to comprehensively identify and quantify proteins in two or more complex samples [1–4]. There are three ways to perform quantitative proteomic analysis: a) the spectral counting method that counts the number of fragment ion spectra for a particular peptide [5]; b) differential stable isotope labeling, in which quantified peptides differ by the mass shifts introduced by the stable isotopes used [6]; and c) labelfree quantification that quantifies the precursor ion signal intensities across different LCMS runs [7–9].
Quantification using the differential stable isotope labeling method is one of the methods for quantification of two or more samples within a single experiment. The technique is based on use of stable isotopes to differentially label proteins or peptides, and on use of mass spectrometry to compare the relative abundance of the proteins in different samples. Over the years, many stable isotope tagging approaches have been developed, which include the ICAT [6], ITRAQ [10], and SILAC [11] approaches. In addition, numerous quantification software were developed, including XPRESS [6], ASAPRatio [12], MSQuant http://msquant.sourceforge.net/, ZoomQuant [13], STEM [14], MultiQ [15], itracker [16], Libra [17], maxQuant [18], muxQuant [19], HTAPP (highthroughput autonomous proteomic pipeline) [20], msInspect [21], the APEX Quantitative Proteomics Tool [22], MASIC [23], and Census [24].
In our quantitative proteomics analysis, we found that errors associated with ratios calculated by the ASAPRatio increased proportionally with the relative abundance ratios of the two isotopic partners. Several factors might have contributed to the increase of relative errors. We found one of the factors to be background noise that was not completely removed by the SavitzkyGolay smooth filtering method.
Wavelets are mathematical functions that divide a given function or a continuoustime signal into different frequency components, and then study each component with a resolution matched to its scale [25, 26]. They have advantages over traditional Fourier transforms in analyzing data for which signals have discontinuities and sharp peaks, and in deconstructing and reconstructing signals more accurately [27].
Various programs integrating wavelet transforms have been developed for analyzing various types of proteomics data, such as MALDI, SELDITOF and LC/MS. Yang et al. compared five smoothing methods used in peak detection algorithms for MALDI mass spectrometry data analysis [28]. They found that the wavelet smoothing performed best among the five smoothing methods: moving average filter, SavitzkyGolay filter, Gaussian filter, Kaiser window, and wavelet based filters [28]. Du et al. showed that a continuous wavelet transform (CWT)based peak detection algorithm enhances the effective signaltonoise ratio in SELDITOF spectra; it could identify both strong and weak peaks while keeping false positive rates low [29]. Randolph and Yasui applied a translationinvariant wavelet analysis to perform multiscale decomposition, feature extraction and quantification for MALDITOF spectra [30]. Alexandrov et al. developed the MALDIDWT program for analyzing serum protein profiles for biomarker discovery [31]. Lange et al. used wavelet techniques to develop a mass spectrometerindependent peakpicking algorithm as an alternative to vendors' peakpicking software bundled with mass spectrometers [32]. SchulzTrieglaff et al. developed an algorithm that uses a mother wavelet to mimic the distribution of isotopic peak intensities [33]. The latter two algorithms by Lange et al. and SchulzTrieglaff et al. were further implemented in OpenMS software [34]. Zhang et al. used an undecimated wavelet transform to remove random noise for prOTOF MS data, which does not require a priori knowledge of protein masses[35]. Using metabolomics data as examples, Tautenhahn et al. developed a new feature detection algorithm centWave for highresolution LC/MS data sets applying continuous wavelet transformation and optional Gaussfitting in the chromatographic domain[36].
Wavelet theory has also been applied to MS data to reduce data dimension or to reduce computation time. For example, Hussong et al. implemented a feature finding algorithm based on a handtailored adaptive wavelet transform that drastically reduces the computation time in mass spectrometry data analysis [37]. Liu et al. used the wavelet detail coefficients to characterize features and reduce the dimensionality of MS data [38].
In this manuscript, we report development of a new wavelet transform algorithm for improved quantitative proteomics analysis. We demonstrate that our approach has an improved ability to smooth isotopic peaks and remove background noise when compared with approaches using other smoothing methods.
Implementation
Technical details of the development of the WaveletQuant program
The wavelet transform is an excellent tool for signal processing because of its denoising ability; one can obtain multiresolution decomposition of signals, while retaining their local characteristic details.
The first step in the wavelet transform method is to choose a proper threshold to denoise signals. The principle of waveletbased denoising is to recognize the noise from the high frequency part of wavelet coefficients. Those coefficients that are less than the threshold are set to zero. Other coefficients are preserved. Then we reconstruct the denoised signals using the new coefficients. As indicated in the Results presented below, setting the wavelet coefficients of noise to zero while at the same time preserving the wavelet coefficients of signals is critical for a successful wavelet transform. Choosing an optimal threshold is the key to retaining maximal true signals while reducing as much noise as possible.
The method is composed of three components: (i) the discrete wavelet transform (DWT) of signal x(t); (ii) setting the threshold for the wavelet coefficients on each scale; and (iii) obtaining denoised signals by inverse wavelet transform based on the threshold wavelet coefficients. A more detailed description of the wavelet transform process is shown in Additional file 1.
Xu et al. [40] proposed a spatially selective noise filtration technique. They declared that the singularity of a signal should have a large peak value in different scales, while noise should have fading energy with increasing scales. Inspired by their work, we developed a 'Spatial Adaptive Algorithm' to identify true peaks (a more detailed description of the method is presented in Additional file 1).
where Corr_{2}(j, n) is denoted as correlation coefficient of the position n in scale j.
Then we compared NewCorr_{2}(j, n) with Wf(j, n) to obtain the edges of important signals. In summary, by multiplying wavelet coefficients of bordered scales, we computed a correlation coefficient to suppress the noise and to strengthen the signal. Our algorithm improved the identification of real signals and the orientational precision of the identified signals.
Software implementation
Result
Application of the WaveletQuant program to data generated using yeast extracts mixed in known ratios
We compared the performance of our WaveletQuant program with the ASAPRatio program using a dataset generated by mixing different ratios of yeast cell extract grown in heavy vs. light isotopic media. Proteins were mixed in the following ratio 1:2, 1:1.5, 1:1, 1.5:1, 2:1, and then analyzed by LTQMS.
Comparison of quantification results between the ASAPRatio and the WaveletQuant programs.
Light/Heavy ratio  Mixed ratio  ASAPRatio ratio  ASAPRatio Relative error (%)  WaveletQuant ratio  WaveletQuant Relative error (%) 

L/H  0.5  0.73  47  0.39  21 
L/H  0.67  0.85  27  0.64  3 
L/H  1  1.51  50  1.09  9 
L/H  1.5  1.2  20  1.48  1 
L/H  2  0.95  52  2.15  7 
Application of the WaveletQuant program to data generated by ICAT for ovarian cancer cell lines
We have previously conducted quantitative proteomics studies comparing cisplatinresistant ovarian cancer cells with cisplatinsensitive cancer cells [41]. Using the RAW data of the cytosolic fractions, we compared TPP with ASAPRatio and TPP with WaveletQuant implementation. We found that TPP with the ASAPRatio was able to quantify the protein expression of 226 proteins, while TPP with WaveletQuant quantified 222 proteins, and 204 proteins were quantified by both algorithms. The total number of proteins quantified combining both programs is 245, which is about 10% more than using either program alone. We found that the average standard deviation for the ratios of quantification were 0.57 for TPP with ASARatio and 0.47 for TPP with WaveletQuant. Thus WaveletQuant appears to have better accuracy for quantification than the ASAPRatio.
Discussion
We developed a new software for quantitative proteomics using the wavelet transform. Mass spectrometry data are usually noisy. In order to better quantify mass spectrometry data, smoothing filters, such as the moving average filter, Gaussian filter Butterworth lowpass filter, and SavitzkyGolay filter can be used to reduce the noise in MS peaks. The moving average filter was used in the MZmine program [42]. The Gaussian filter was used by the local maximum search (LMS) program, which was developed for SELDI MS data analysis [43]. The smoothing used in the XPRESS program was performed with the Butterworth lowpass filter http://www.qsl.net/kp4md/butrwrth.htm, for which lowfrequency excitation signal components down to and including the current ones are transmitted, while highfrequency components, up to and including infinite ones, are blocked. The ASAPRatio program uses the SavitzkyGolay method [12], which performs a least squares fit of a small set of consecutive data points to a polynomial and then takes the central point of the fitted polynomial curve as the output. The SavitzkyGolay smoothing tends to preserve features of the distribution such as relative maxima, minima, and width; this is its main advantage as these features are often 'flattened' by other smoothing methods (e.g. moving averages). However, as we showed in Results, a disadvantage of the SavitzkyGolay filter is that it smoothes signals by increasing window sizes and lowering filter frequencies; thus, the smoothed shape could create poor representations of true signals and generate inaccurate quantification. We found that wavelet smoothing is better than the SavitzkyGolay filter used with ASAPRatio. Yang et al. similarly found that wavelet smoothing performed better than moving average filter, SavitzkyGolay filter, Gaussian filter, and Kaiser window [28].
In addition, we implemented orthogonal wavelets to decompose signals in our WaveletQuant program. The wavelet transform is different from that used by Lange et al. and SchulzTrieglaff et al. [32, 33]. Many wavelets could be chosen to perform wavelet transform, including Daubechies' orthogonal and biorthogonal wavelets, Gaussian wavelets and coiflets [25]. Each wavelet has its own advantage depending on wavelet shapes and wavelet widths. The orthogonal wavelet can keep the energy (i.e. sum of squares of coefficients, usually referred to as "energy" in the signal processing field) of a signal unchanged. We have therefore selected the orthogonal wavelet transform for our MS data analysis.
We implemented two methods. First, by combining the advantage of hard threshold and soft threshold, we developed the waveletbased signal threshold denoising algorithm to distinguish signals from noise in MS data. Second, we developed the spatial adaptive algorithm, which not only was effective in removing high frequency noise but also was effective for low frequency denoising. Combining these two algorithms, our WaveletQuant program performs better than the ASAPRatio program on the datasets from yeast that we tested (Figures 2 and 3). Finally, in a test using high throughput proteomics data generated from cell lysates in an ovarian cancer study, we found that the ratios obtained by our program have lower overall standard deviation than that obtained by the ASAPRatio.
Of note, we also mixed proteins in 1:4 and 4:1 ratios and analyzed them by LTQMS. However, due to the limited dynamic range of the routine LC/MS that we performed, the average ratios calculated by both the ASAPRatio and the WaveletQuant programs were faroff from the original mixed ratios, with large standard deviation. This is not surprising as the mixed ratios are outside the dynamic range of a routine LC/MS analysis, which Canterbury et al. estimated to be 0.5 to 2.5 in a systematic analysis [44]. This result also suggests that our WaveletQuant program did not improve the dynamic range of the quantification. Another possibility is that the experiment failed due to unknown reasons. Therefore, we have not included the data in this report.
Finally, we have implemented our wavelet transform algorithm and developed the WaveletQuant program. As the TPP pipeline is widely used in proteomic data analysis, we incorporated WaveletQuant software into the TPP pipeline http://tools.proteomecenter.org/TPP.php. Users can employ the WaveletQuant implemented TPP pipeline as an alternative to the standard TPP pipeline.
Conclusions
We have developed an improved and/or alternative program for quantitative proteomics analysis, which is implemented in the standard TPP pipeline for the convenience of users.
Availability and requirements

Project name: WaveletQuant

Project home page:http://www.zcni.zju.edu.cn/en/WaveletQuant_for_Quantitative_Proteomics/waveletquant.html or http://systemsbiozju.org/data/WaveletQuant.

Operating systems: Windows 2000, Windows XP or higher

Programming languages: MSVC++ 7.1 or higher

Other requirements: None

License: This is a free software. You can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation.
Notes
Abbreviations
 LC:

Liquid Chromatography
 MS:

Mass Spectrometry
 LTQ:

Linear ion Trap Quadrupole
 MALDI:

Matrix Assisted Laser Desorption/Ionization
 SELDI:

Surface Enhanced Laser Desorption/Ionization
 TOF:

Time Of Flight
 ICAT:

Isotope Coded Affinity Tagging
 ITRAQ:

Isobaric Tag for Relative and Absolute Quantitation
 SILAC:

Stable Isotope Labeling with Amino Acids in Cell Culture
 DWT:

Discrete Wavelet Transform
 CWT:

Continuous Wavelet Transform
 LSM:

Local Maximum Search.
Declarations
Acknowledgements
We thank Dan Martin and David Shteynberg at the Institute for Systems Biology for sharing with us the data from the control yeast mixture proteomics experiments for testing this software. This work is partly supported by NSF of China (10771190 and 10971189), grants from the Ministry of Science and Technology (2006AA02Z4A2, 2006AA02A303, 2006DFA32950 and 2007DFC30360), the Doctoral Program Foundation of Ministry of Education of China (20070335176), and the grants MEDC GR687 (Michigan Proteomics Alliance for Cancer Research) and U54DA 021519 (NCIBI) from NIH, USA.
Authors’ Affiliations
References
 Aebersold R, Mann M: Mass spectrometrybased proteomics. Nature 2003, 422(6928):198–207. 10.1038/nature01511View ArticlePubMed
 Ong SE, Mann M: Mass spectrometrybased proteomics turns quantitative. Nat Chem Biol 2005, 1(5):252–262. 10.1038/nchembio736View ArticlePubMed
 Qian WJ, Jacobs JM, Liu T, Camp DG II, Smith RD: Advances and challenges in liquid chromatographymass spectrometrybased proteomics profiling for clinical applications. Mol Cell Proteomics 2006, 5(10):1727–1744. 10.1074/mcp.M600162MCP200View ArticlePubMedPubMed Central
 Mueller LN, Brusniak MY, Mani DR, Aebersold R: An assessment of software solutions for the analysis of mass spectrometry based quantitative proteomics data. J Proteome Res 2008, 7(1):51–61. 10.1021/pr700758rView ArticlePubMed
 Liu H, Sadygov RG, Yates JR III: A model for random sampling and estimation of relative protein abundance in shotgun proteomics. Anal Chem 2004, 76(14):4193–4201. 10.1021/ac0498563View ArticlePubMed
 Han DK, Eng J, Zhou H, Aebersold R: Quantitative profiling of differentiationinduced microsomal proteins using isotopecoded affinity tags and mass spectrometry. Nat Biotechnol 2001, 19(10):946–951. 10.1038/nbt1001946View ArticlePubMedPubMed Central
 Mueller LN, Rinner O, Schmidt A, Letarte S, Bodenmiller B, Brusniak MY, Vitek O, Aebersold R, Muller M: SuperHirn  a novel tool for high resolution LCMSbased peptide/protein profiling. Proteomics 2007, 7(19):3470–3480. 10.1002/pmic.200700057View ArticlePubMed
 Hwang D, Zhang N, Lee H, Yi E, Zhang H, Lee IY, Hood L, Aebersold R: MSBID: a Java package for labelfree LCMSbased comparative proteomic analysis. Bioinformatics 2008, 24(22):2641–2642. 10.1093/bioinformatics/btn491View ArticlePubMedPubMed Central
 Andreev VP, Li L, Cao L, Gu Y, Rejtar T, Wu SL, Karger BL: A new algorithm using crossassignment for labelfree quantitation with LCLTQFT MS. J Proteome Res 2007, 6(6):2186–2194. 10.1021/pr0606880View ArticlePubMedPubMed Central
 Aggarwal K, Choe LH, Lee KH: Shotgun proteomics using the iTRAQ isobaric tags. Brief Funct Genomic Proteomic 2006, 5(2):112–120. 10.1093/bfgp/ell018View ArticlePubMed
 Ong SE, Foster LJ, Mann M: Mass spectrometricbased approaches in quantitative proteomics. Methods 2003, 29(2):124–130. 10.1016/S10462023(02)003031View ArticlePubMed
 Li X, Zhang H, Ranish JA, Aebersold R: Automated Statistical Analysis of Protein Abundance Ratios from Data Generated by StableIsotope Dilution and Tandem Mass Spectrometry. ANALYTICAL CHEMISTRYWASHINGTON DC 2003, 75(23):6648–6657.View Article
 Halligan BD, Slyper RY, Twigger SN, Hicks W, Olivier M, Greene AS: ZoomQuant: an application for the quantitation of stable isotope labeled peptides. J Am Soc Mass Spectrom 2005, 16(3):302–306. 10.1016/j.jasms.2004.11.014View ArticlePubMedPubMed Central
 Shinkawa T, Taoka M, Yamauchi Y, Ichimura T, Kaji H, Takahashi N, Isobe T: STEM: a software tool for largescale proteomic data analyses. J Proteome Res 2005, 4(5):1826–1831. 10.1021/pr050167xView ArticlePubMed
 Lin WT, Hung WN, Yian YH, Wu KP, Han CL, Chen YR, Chen YJ, Sung TY, Hsu WL: MultiQ: a fully automated tool for multiplexed protein quantitation. J Proteome Res 2006, 5(9):2328–2338. 10.1021/pr060132cView ArticlePubMed
 Shadforth IP, Dunkley TP, Lilley KS, Bessant C: iTracker: for quantitative proteomics using iTRAQ. BMC Genomics 2005, 6: 145. 10.1186/147121646145View ArticlePubMedPubMed Central
 Keller A, Eng J, Zhang N, Li XJ, Aebersold R: A uniform proteomics MS/MS analysis platform utilizing open XML file formats. Mol Syst Biol 2005, 1: 2005–0017. 10.1038/msb4100024View ArticlePubMedPubMed Central
 Cox J, Mann M: MaxQuant enables high peptide identification rates, individualized p.p.b.range mass accuracies and proteomewide protein quantification. Nat Biotechnol 2008, 26(12):1367–1372. 10.1038/nbt.1511View ArticlePubMed
 Palmblad M, Mills DJ, Bindschedler LV: Heatshock response in Arabidopsis thaliana explored by multiplexed quantitative proteomics using differential metabolic labeling. J Proteome Res 2008, 7(2):780–785. 10.1021/pr0705340View ArticlePubMed
 Yu K, Sabelli A, DeKeukelaere L, Park R, Sindi S, Gatsonis CA, Salomon A: Integrated platform for manual and highthroughput statistical validation of tandem mass spectra. Proteomics 2009, 9(11):3115–3125. 10.1002/pmic.200800899View ArticlePubMedPubMed Central
 May D, Law W, Fitzgibbon M, Fang Q, McIntosh M: Software platform for rapidly creating computational tools for mass spectrometrybased proteomics. J Proteome Res 2009, 8(6):3212–3217. 10.1021/pr900169wView ArticlePubMedPubMed Central
 Braisted JC, Kuntumalla S, Vogel C, Marcotte EM, Rodrigues AR, Wang R, Huang ST, Ferlanti ES, Saeed AI, Fleischmann RD, et al.: The APEX Quantitative Proteomics Tool: generating protein quantitation estimates from LCMS/MS proteomics results. BMC Bioinformatics 2008, 9: 529. 10.1186/147121059529View ArticlePubMedPubMed Central
 Monroe ME, Shaw JL, Daly DS, Adkins JN, Smith RD: MASIC: a software program for fast quantitation and flexible visualization of chromatographic profiles from detected LCMS(/MS) features. Comput Biol Chem 2008, 32(3):215–217. 10.1016/j.compbiolchem.2008.02.006View ArticlePubMedPubMed Central
 Park SK, Venable JD, Xu T, Yates JR III: A quantitative analysis software tool for mass spectrometrybased proteomics. Nat Methods 2008, 5(4):319–322.PubMedPubMed Central
 Meyer Y: Wavelets: Algorithms and Applications. Philadelphia: Society for Industrial and Applied Mathematics; 1993.
 Mallat SG: A theory for multiresolution signal decomposition: the waveletrepresentation. Pattern Analysis and Machine Intelligence, IEEE Transactions on 1989, 11(7):674–693. 10.1109/34.192463View Article
 Crandall R: Projects in Scientific Computation. New York: SpringerVerlag; 1994.View Article
 Yang C, He Z, Yu W: Comparison of public peak detection algorithms for MALDI mass spectrometry data analysis. BMC Bioinformatics 2009, 10: 4. 10.1186/14712105104View ArticlePubMedPubMed Central
 Du P, Kibbe WA, Lin SM: Improved peak detection in mass spectrum by incorporating continuous wavelet transformbased pattern matching. Bioinformatics 2006, 22(17):2059. 10.1093/bioinformatics/btl355View ArticlePubMed
 Randolph TW, Yasui Y: Multiscale processing of mass spectrometry data. Biometrics 2006, 62(2):589–597. 10.1111/j.15410420.2005.00504.xView ArticlePubMed
 Alexandrov T, Decker J, Mertens B, Deelder AM, Tollenaar RA, Maass P, Thiele H: Biomarker discovery in MALDITOF serum protein profiles using discrete wavelet transformation. Bioinformatics 2009, 25(5):643–649. 10.1093/bioinformatics/btn662View ArticlePubMedPubMed Central
 Lange E, Gropl C, Reinert K, Kohlbacher O, Hildebrandt A: Highaccuracy peak picking of proteomics data using wavelet techniques. Pac Symp Biocomput 2006, 11: 243–254. full_text
 SchulzTrieglaff O, Hussong R, Gropl C, Leinenbach A, Hildebrandt A, Huber C, Reinert K: Computational quantification of peptides from LCMS data. J Comput Biol 2008, 15(7):685–704. 10.1089/cmb.2007.0117View ArticlePubMed
 Sturm M, Bertsch A, Gropl C, Hildebrandt A, Hussong R, Lange E, Pfeifer N, SchulzTrieglaff O, Zerck A, Reinert K, et al.: OpenMS  an opensource software framework for mass spectrometry. BMC Bioinformatics 2008, 9: 163. 10.1186/147121059163View ArticlePubMedPubMed Central
 Zhang S, DeGraba TJ, Wang H, Hoehn GT, Gonzales DA, Suffredini AF, Ching WK, Ng MK, Zhou X, Wong ST: A novel peak detection approach with chemical noise removal using shorttime FFT for prOTOF MS data. Proteomics 2009, 9(15):3833–3842. 10.1002/pmic.200800030View ArticlePubMedPubMed Central
 Tautenhahn R, Bottcher C, Neumann S: Highly sensitive feature detection for high resolution LC/MS. BMC Bioinformatics 2008, 9: 504. 10.1186/147121059504View ArticlePubMedPubMed Central
 Hussong R, Gregorius B, Tholey A, Hildebrandt A: Highly accelerated feature detection in proteomics data sets using modern graphics processing units. Bioinformatics 2009, 25(15):1937–1943. 10.1093/bioinformatics/btp294View ArticlePubMed
 Liu Y: Feature extraction and dimensionality reduction for mass spectrometry data. Comput Biol Med 2009, 39(9):818–823. 10.1016/j.compbiomed.2009.06.012View ArticlePubMed
 Donoho DL, Johnstone JM: Ideal spatial adaptation by wavelet shrinkage. Biometrika 1994, 81: 425–455. 10.1093/biomet/81.3.425View Article
 Xu Y, Weaver JB, Healy DM, Lu J: Wavelet transform domain filters: a spatially selective noise filtration technique. Image Processing, IEEE Transactions on 1994, 3(6):747–758. 10.1109/83.336245View Article
 Stewart JJ, White JT, Yan X, Collins S, Drescher CW, Urban ND, Hood L, Lin B: Proteins associated with Cisplatin resistance in ovarian cancer cells identified by quantitative proteomic technology and integrated with mRNA expression levels. Mol Cell Proteomics 2006, 5(3):433–443.View ArticlePubMed
 Katajamaa M, Miettinen J, Oresic M: MZmine: toolbox for processing and visualization of mass spectrometry based molecular profile data. Bioinformatics 2006, 22(5):634–636. 10.1093/bioinformatics/btk039View ArticlePubMed
 Yasui Y, Pepe M, Thompson ML, Adam BL, Wright GL Jr, Qu Y, Potter JD, Winget M, Thornquist M, Feng Z: A dataanalytic strategy for protein biomarker discovery: profiling of highdimensional proteomic data for cancer detection. Biostatistics 2003, 4(3):449–463. 10.1093/biostatistics/4.3.449View ArticlePubMed
 Canterbury JD, Yi X, Hoopmann MR, MacCoss MJ: Assessing the dynamic range and peak capacity of nanoflow LCFAIMSMS on an ion trap mass spectrometer for proteomics. Anal Chem 2008, 80(18):6888–6897. 10.1021/ac8004988View ArticlePubMedPubMed Central
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.