基于組合濾波的魚油二十碳五烯酸含量近紅外光譜檢測

蔡劍華，胡惟文，王先春（湖南文理學(xué)院信息研究所，常德415000）

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基于組合濾波的魚油二十碳五烯酸含量近紅外光譜檢測

蔡劍華，胡惟文，王先春
（湖南文理學(xué)院信息研究所，常德415000）

摘要：為了提高魚油二十碳五烯酸（eicosapentaenoic acid, EPA）含量的測定精度，該研究將經(jīng)驗?zāi)B(tài)分解（empirical mode decomposition，EMD）和數(shù)學(xué)形態(tài)學(xué)濾波相結(jié)合的近紅外光譜去噪方法應(yīng)用于魚油的一階導(dǎo)數(shù)光譜預(yù)處理中，給出了方法的原理和步驟，評估了該方法的去噪效果。運用偏最小二乘回歸（partial least squares regression, PLSR）建立了魚油EPA近紅外光譜的預(yù)測模型，用處理后的光譜計算了魚油中EPA的含量，并與九點平滑和小波變換方法的處理結(jié)果進行了對比分析。結(jié)果表明：與傳統(tǒng)的九點平滑處理結(jié)果相比，信噪比（signal to noise ratio，SNR）從14 dB左右提高到35 dB左右，原始信號與消噪信號之間的標(biāo)準(zhǔn)差由0.005 71降到0.002 26；預(yù)測集的決定系數(shù)由0.959 3提高到0.987 9，預(yù)測均方根誤差（root mean square error, RMSE）由0.060 1降為0.031 2。證明了組合的EMD和數(shù)學(xué)形態(tài)學(xué)濾波方法在光譜處理過程中的可靠性，提高了魚油EPA含量近紅外光譜的定量分析精度。

關(guān)鍵詞：光譜測定；模型；經(jīng)驗?zāi)B(tài)分解；數(shù)學(xué)形態(tài)濾波；近紅外光譜；魚油；去噪

蔡劍華，胡惟文，王先春.基于組合濾波的魚油二十碳五烯酸含量近紅外光譜檢測[J].農(nóng)業(yè)工程學(xué)報，2016，32（01）：312-317.doi：10.11975/j.issn.1002-6819.2016.01.043 http://www.tcsae.org

Cai Jianhua, Hu Weiwen, Wang Xianchun.Near-infrared spectrum detection of fish oil eicosapentaenoic acid content based on combinational filtering[J].Transactions of the Chinese Society of Agricultural Engineering（Transactions of the CSAE）, 2016, 32 （01）: 312－317.（in Chinese with English abstract）doi：10.11975/j.issn.1002-6819.2016.01.043 http://www.tcsae.org

0　引言

Dyerber等人發(fā)現(xiàn)魚油中所含二十碳五烯酸（eicosapentaenoic acid，EPA）和二十二碳六烯酸（docosahexaenoic acid，DHA）具有抗血栓和抗動脈硬化的醫(yī)藥作用，從此魚油制藥品和食品深受人們的喜愛和關(guān)注[1-2]。近幾年來，近紅外光譜分析技術(shù)成為了對魚油中的EPA和DHA進行定性、定量分析研究的重要手段[2]。但在背景噪聲下，魚油吸收光譜的部分譜峰往往會被噪聲淹沒，難以辨別，而有價值的信息多以特征峰或相關(guān)峰形式存在[2-3]。所以為了凸顯光譜的峰值信息，需要對光譜數(shù)據(jù)進行去噪處理，提高其信噪比。常用的平滑濾波方法有丟失光譜信號高頻特征的缺陷[4-5]。小波變換和經(jīng)驗?zāi)B(tài)分解（empirical mode decomposition，EMD）近幾年來被廣泛應(yīng)用到光譜的去噪中，取得了不錯的效果，但仍存在不足，如：小波方法中的小波函數(shù)的選擇，分解層數(shù)的確定[4-7]，EMD分解中的模態(tài)混疊等[8]。本文結(jié)合EMD與數(shù)學(xué)形態(tài)學(xué)濾波各自的優(yōu)點，提出了一種光譜預(yù)處理方法，并首次將它引入到魚油EPA含量近紅外光譜檢測中來，探索一種提高近紅外光譜測定魚油EPA含量的新方法。

1　材料與方法

1.1經(jīng)驗?zāi)B(tài)分解和數(shù)學(xué)形態(tài)學(xué)基本變換

經(jīng)驗?zāi)B(tài)分解，由美籍華人科學(xué)家諾頓·黃提出，又叫Huang變換，它能將信號分解為一組固有模態(tài)函數(shù)（intrinsic mode function，IMF）和的形式，是一個從高頻到低頻的自適應(yīng)過程，具體實現(xiàn)步驟見文獻[9-10，12]。數(shù)學(xué)形態(tài)學(xué)是由一組形態(tài)學(xué)算子組成，形態(tài)學(xué)的基本運算包括腐蝕、膨脹、開和閉。噪聲通常是在一定范圍內(nèi)作為一個峰值（“峰頂”或“谷低”）疊加在信號里面，而形態(tài)學(xué)的開操作可以用來剝離“峰頂”的噪聲，形態(tài)學(xué)的閉操作可以用來填充“谷低”的噪聲，二者都有濾波功能[13-15]。在實際應(yīng)用中，開啟和關(guān)閉操作經(jīng)常結(jié)合形成形態(tài)學(xué)濾波算法。文章使用的廣義形態(tài)濾波器是基于廣義開-閉和閉-開運算來定義的，具體推導(dǎo)過程見文獻[14，16]，此處不再累述。

1.2預(yù)處理流程

基于EMD和數(shù)學(xué)形態(tài)學(xué)濾波的導(dǎo)數(shù)光譜預(yù)處理流程如圖1所示。根據(jù)圖1，方法與步驟可描述如下：

1）根據(jù)EMD方法，導(dǎo)數(shù)光譜被分解為一系列的模態(tài)函數(shù)IMFs，包括高階模態(tài)函數(shù)h（n）和低階模態(tài)函數(shù)l（n），接著將高頻部分和低頻部分分開，分別進行去噪處理。

2）對于低階模態(tài)函數(shù)l（n），首先采用數(shù)學(xué)形態(tài)學(xué)濾波方法對其進行處理得到消噪后的部分g（n），然后用l（n）減去g（n），得到峰值信號f（n）。對于f（n），為了盡可能多保留光譜數(shù)據(jù)的有用成分，再用自適應(yīng)閾值去噪方法對其進行二次分離，得到結(jié)果為f′（n）。最后，g（n）和f′（n）相加，其和就為低階模態(tài)函數(shù)的去噪結(jié)果l′（n）。

3）對于高階模態(tài)函數(shù)h（n），采用平滑濾波來消除基線漂移，得到濾波結(jié)果h′（n），將第2步和第3得到的去噪結(jié)果l′（n）和h′（n）相加，其和就視為原始導(dǎo)數(shù)光譜的去噪結(jié)果。

4）將去噪后的光譜數(shù)據(jù)與魚油中的EPA等化學(xué)成分的基礎(chǔ)數(shù)據(jù)進行關(guān)聯(lián)，用定量分析軟件Unscrambler建立模型，采用偏最小二乘法和交叉驗證法，分析魚油中的EPA含量。

圖1　基于EMD和數(shù)學(xué)形態(tài)學(xué)濾波的光譜預(yù)處理流程圖Fig.1 Flow-process diagram of pretreatment of near-infrared spectrum based on combinatorial method

1.3光譜數(shù)據(jù)采集

使用的便攜式近紅外光譜儀為：Mini-AOTF/（NIR），型號：Luminar5030，廠家：美國BRIMROSE公司。儀器波長范圍為：1 300～2 300 nm，波長增量為：2 nm，掃描次數(shù)為：600。共標(biāo)記48個樣品，隨機選用28個標(biāo)記為校正集，20個為驗證集，48個魚油樣品采用漫反射的測樣方式采集光譜。各濾波方法、偏最小二乘回歸（partial least squares regression, PLSR）、統(tǒng)計分析在Unscrambler 9.8和Matlab 7.0.1中實現(xiàn)。采集到的48個魚油樣品的原始光譜和一階導(dǎo)數(shù)光譜如圖2所示?？梢?原始光譜比較光滑，但基線漂移較嚴(yán)重；導(dǎo)數(shù)光譜消除了基線漂移，但求導(dǎo)使隨機誤差也被放大，使信噪比顯著降低，需要進行去噪處理。

圖2　48個魚油樣品的原始光譜和一階導(dǎo)數(shù)譜Fig.2 Original spectrum and first derivative spectrum of 48 fish oil sample

1.4預(yù)處理效果評價參數(shù)

對于光譜的去噪，通常要求在去噪后光譜曲線的特征位置和形狀保持不變，并盡可能使曲線平滑[17]。為了探討本文方法對近紅外光譜的去噪效果，采用了信噪比（signal to noiseratio，SNR）、均方誤差（rootmeansquareerror，RMSE）、橫向特征保持指數(shù)（horizontal feature remain index，HFRI）和縱向特征保持指數(shù)（vertical feature remain index，VFRI）4項指標(biāo)來對魚油光譜去噪效果進行評估。用SNR和RMSE來反映方法的去噪能力；用光譜特征波段處的HFRI和VFRI來評價方法對光譜特征的保持能力。4個指標(biāo)參數(shù)的計算如（1）-（4）式所示[18-21]。

橫向特征保持指數(shù)：

縱向特征保持指數(shù)：

式（1）-式（4）中，f（mi）和表示去噪前后的光譜數(shù)據(jù)，i=1，2，…，N，N為波段數(shù)，i表示波段位置，（3）式表示以原始特征位置i為中心。

2　結(jié)果與分析

2.1魚油光譜去噪

先以8號樣品光譜為例，對魚油光譜進行消噪處理，以評價本文方法的有效性。圖3（a）為8號樣品原始光譜圖，可見所示光譜譜峰特征不夠明顯，往往為了提高光譜分析精度，需要對原始光譜進一步求導(dǎo)。圖3（b）為8號樣品一階導(dǎo)數(shù)光譜圖。由譜圖可以看到，求導(dǎo)后光譜特征變得明顯，光譜吸收峰變窄，但導(dǎo)數(shù)光譜也帶來些新問題，降低了光譜信噪比，所以需要進一步進行消噪處理。

文章分別采用4種方法對光譜進行消噪預(yù)處理：9點多動平滑法、25點移動平滑法、小波軟閾值去噪法（Heursure閾值）[22-23]和本文方法。采用4種方法對8號樣品導(dǎo)數(shù)光譜去噪后的效果如圖3（c）－圖3（f）所示。光譜曲線濾波后，分別計算4項評價指標(biāo)。首先計算去噪后光譜的SNR和RMSE；接著選取特征波段的位置計算特征保持指數(shù)HFRI和VFRI。本文以圖3中明顯吸收波段的位置作為特征波段，分別為以1 396、1 718、1 765、2 109、2 230 nm為中心，前后各5 nm作為有效范圍，共5段。表1分別列出了幾種去噪方法的4個評價參數(shù)的對照值。

圖3　8號樣品幾種去噪方法的去噪結(jié)果比較Fig.3 Comparison of several de-noising methods for the spectrum of No.8 sample

由圖3和表1可以看出：1）移動平滑法有效地去除了高頻噪聲，導(dǎo)數(shù)光譜SNR被提高，但也丟失了較多的有效信息，導(dǎo)致特征位置橫向和縱向保持能力較差，其平滑效果和特征保持都不好，但隨著平滑窗口的增大，光譜圖形越光滑；2）小波軟閾值方法去噪后對光譜的峰形影響不大，兩個評價參數(shù)中，信噪比達到29 dB，而均方根誤差僅為0.003左右，而且特征保持的也相對較好，是較好的濾波方法。3）形態(tài)小波的去噪效果較好，導(dǎo)數(shù)光譜噪聲基本得到去除。4）本文提出的基于EMD和數(shù)學(xué)形態(tài)學(xué)濾波的方法去噪效果優(yōu)于其他方法。其均方根誤差僅為0.002 26，而信噪比達到了35.785，也很好保留了光譜信號的特征尖峰點，且橫向特征保持指數(shù)（HFRI）和縱向特征保持指數(shù)（VFRI）都比其他幾種方法好，體現(xiàn)了本文方法具有良好的細節(jié)保留和抗噪聲性能。

表1　8號樣品光譜幾種消噪方法信噪比、均方根誤差、波形橫向特征保持指數(shù)和縱向特征保持指數(shù)對比Table 1 Comparison of several de-noising methods for SNR，RMSE，HFRI and VFRI

對其他47個樣品的光譜也采用相同的方法做了消噪處理。圖4對比了48個魚油樣品光譜經(jīng)小波變換處理和本文方法處理后的去噪效果（由于小波閾值方法較平滑法去噪效果好，且為光譜預(yù)處理中常用的方法，為節(jié)約篇幅，此處僅給出小波軟閾值方法與本文方法的對比）。從圖4可以看出，小波閾值去噪方法消噪效果較好，對峰形也沒有太大影響；基于EMD和數(shù)學(xué)形態(tài)學(xué)濾波的方法消噪效果更好些（對照始端和末端的光譜曲線可見），噪聲得到了很好的抑制，且光譜的峰形沒有太大變化，特征尖峰保留的很好。

圖4　48個魚油樣品一階導(dǎo)數(shù)近紅外光譜去噪效果對比Fig.4　 First derivative spectrum of 48 fish oil samples from different de-noising method

2.2EPA含量檢測

從所采集48個魚油樣本中，隨機選取20個樣本，分別采用9點平滑法、小波軟閾值、形態(tài)小波和本文方法對光譜進行去噪處理，將經(jīng)過預(yù)處理后的光譜數(shù)據(jù)與魚油中的EPA等化學(xué)成分的基礎(chǔ)數(shù)據(jù)進行關(guān)聯(lián)，分析魚油中的EPA含量，以比較不同濾波方法對魚油EPA含量檢測的影響。用預(yù)測集中的決定系數(shù)（r2）和均方根誤差（RMSE）來評價各去噪方法的優(yōu)劣。從比較的結(jié)果得到：基于EMD和數(shù)學(xué)形態(tài)學(xué)濾波的方法是有效的，與常用的9點平滑濾波法處理結(jié)果相比，預(yù)測均方根誤差RMSE由0．060 1降為0．031 2，預(yù)測集的決定系數(shù)r2由0．959 3提高到0．987 9，其處理效果相比小波軟閾值方法及形態(tài)小波方法也更理想些，有效地提高了光譜的分析精度。

3　結(jié)論

1）文章將經(jīng)驗?zāi)B(tài)分解與數(shù)學(xué)形態(tài)學(xué)濾波相結(jié)合，應(yīng)用在魚油近紅外光譜預(yù)處理階段，對比和參數(shù)評價表明該方法結(jié)合了兩者的優(yōu)點，是切實可行和有效的。

2）實驗表明本文方法在真實保留魚油光譜信號細節(jié)的前提下，極大程度的衰減了噪聲，改善了魚油吸收光譜信號較弱、造成部分譜峰淹沒在噪聲中難以辨別的現(xiàn)象，有效的改善了光譜質(zhì)量，有助于后續(xù)魚油成分分析的光譜建模。

3）本文方法與傳統(tǒng)的9點平滑法相比，預(yù)測均方根誤差RMSE由0.060 1降為0.031 2，預(yù)測集的決定系數(shù)r2由0.959 3提高到0.987 9，其處理效果相比小波軟閾值方法及形態(tài)小波方法也更理想些，提高了模型預(yù)測精度。

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Near-infrared spectrum detection of fish oil eicosapentaenoic acid content based on combinational filtering

Cai Jianhua, Hu Weiwen , Wang Xianchun
（Information Institute, Hunan University of Arts and Science, Changde, 415000, China）

Abstract:The near-infrared（NIR）spectral analysis technology has become an important method in the qualitative and quantitative analysis of the composition of fish oil.Yet the absorption spectrum signal of fish oil is generally weak.Especially, when the NIR spectrum is applied to the component analysis, part of the spectrum peaks are often submerged in the noise and difficult to be identified.In order to improve the accuracy of non-destructive detection of eicosapentaenoic acid（EPA）content of fish oil, a combined method was proposed to conduct the pretreatment of fish oil NIR spectrum based on the empirical mode decomposition（EMD）and the morphological filtering.The principle and steps of the method were given.Firstly, derivative spectra were decomposed into a series of modal functions based on the EMD, including high-order and low-order modal function.Then the high-order part and low-order part were separated to deal with respectively.For low-order modal function, the mathematical morphology filtering method and the adaptive threshold de-noising method were used to de-noise to retain useful spectral data as much as possible.For high-order modal function, smoothing filter was used to eliminate baseline drift.Then the sum of 2 parts was determined as the de-noised spectrum.Finally, after de-noising, the correlation analysis was conducted between spectral data and the EPA chemical composition data in fish oil.The partial least squares regression was adopted to establish the prediction model, and the EPA content of fish oil was calculated from the de-noised spectrum.The spectra of 48 fish oil samples were collected using a portable NIR spectrometer（Mini-AOTF/（NIR））, which was produced by Brimrose company in the United States of America.The model of the NIR spectrometer was Luminar 5030, the wavelength range was 2 300～1 300 nm, the wavelength increment was 2 nm and the scanning time was 600.Randomly, 28 fish oil samples were selected and marked as calibration set, and 20 fish oil samples were selected as validation set.The nine-point smoothing method, the wavelet soft-threshold, the morphological wavelet and the proposed method were respectively used as pretreatment method to deal with the spectrum.Then the EPA content of fish oil was calculated based on the de-noised spectrum and a comparative analysis of their results was conducted.The filtering method and the statistical analysis were implemented in Matlab 7.0.1.The result of the presented method was compared with that of the nine-point smoothing method which was the most traditional method.It could be seen that the signal-noise ratio（SNR）was improved from 14 to 35 dB, and the root mean square error （RMSE）between raw signal and de-noised signal was reduced from 0.005 71 to 0.002 26.These embodied the proposed method had a good performance in the retention and resistance to noise.The determination coefficient of the prediction set was improved from 0.959 3 to 0.987 9, and the RMSE was reduced from 0.060 1 to 0.031 2.The model prediction accuracy was improved.And the treatment effect was also better than the wavelet soft-threshold method or the morphological wavelet method which were widely used in the preprocessing of the spectrum.The experimental results showed that the proposed method combined the advantages of EMD and mathematical morphology filter.Under the premise that real details of fish oil spectrum signal were kept, the noise was attenuated at the maximum degree.After de-noising, the spectrum peak which was submerged in noise became clear and easy to be identified, and the quality of spectrum data was improved effectively.These improve that the proposed combined method is effective to conduct the pretreatment of NIR spectrum of fish oil and improves the accuracy of NIR spectrum detection of fish oil EPA content.The combination of EMD and morphological filtering also provides a new way for NIR spectra de-noising.

Keywords:spectrometry; models; empirical mode decomposition; morphological filtering; near-Infrared spectrum; fish oil; de-noising

作者簡介：蔡劍華，男，湖南桂陽人，副教授，博士，主要從光電信號處理等方面的研究工作。常德湖南文理學(xué)院信息研究所，415000。Email: cjh1021cjh@163.com

基金項目：國家自然科學(xué)基金項目（41304098）；湖南省教育廳青年項目（13B076）；湖南省重點建設(shè)學(xué)科-光學(xué)基金；湖南文理學(xué)院博士啟動項目。

收稿日期：2015-07-26

修訂日期：2015-11-17

中圖分類號：O657.3

文獻標(biāo)志碼：A

文章編號：1002-6819（2016）-01-0312-06

doi：10.11975/j.issn.1002-6819.2016.01.043