Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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Decision function for optimal smoothing parameter of asymmetrically reweighted penalized least squares

Asymetrically reweighted penalized least squares에서 최적의 평활화 매개변수를 위한 결정함수

  • Park, Aa-Ron (School of Electronics and Computer Engineering, Chonnam National University) ;
  • Park, Jun-Kyu (Korea Institute of Industrial Technology) ;
  • Ko, Dae-Young (School of Electronics and Computer Engineering, Chonnam National University) ;
  • Kim, Sun-Geum (School of Electronics and Computer Engineering, Chonnam National University) ;
  • Baek, Sung-June (School of Electronics and Computer Engineering, Chonnam National University)
  • 박아론 (전남대학교 전자컴퓨터공학부) ;
  • 박준규 (한국생산기술연구원) ;
  • 고대영 (전남대학교 전자컴퓨터공학부) ;
  • 김순금 (전남대학교 전자컴퓨터공학부) ;
  • 백성준 (전남대학교 전자컴퓨터공학부)
  • Received : 2018.11.28
  • Accepted : 2019.03.08
  • Published : 2019.03.31
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Abstract

In this study, we present a decision function of optimal smoothing parameter for baseline correction using Asymmetrically reweighted penalized least squares (arPLS). Baseline correction is very important due to influence on performance of spectral analysis in application of spectroscopy. Baseline is often estimated by parameter selection using visual inspection on analyte spectrum. It is a highly subjective procedure and can be tedious work especially with a large number of data. For these reasons, an objective procedure is necessary to determine optimal parameter value for baseline correction. The proposed function is defined by modeling the median value of possible parameter range as the length and order of the background signal. The median value increases as the length of the signal increases and decreases as the degree of the signal increases. The simulated data produced a total of 112 signals combined for the 7 lengths of the signal, adding analytic signals and linear and quadratic, cubic and 4th order curve baseline respectively. According to the experimental results using simulated data with linear, quadratic, cubic and 4th order curved baseline, and real Raman spectra, we confirmed that the proposed function can be effectively applied to optimal parameter selection for baseline correction using arPLS.

본 연구에서는 arPLS(asymmetrically reweighted penalized least squares) 방법에서 분광신호의 길이와 차수를 이용한 최적의 평활화 매개변수를 위한 결정함수를 제안한다. 분광신호의 기준선 보정은 분석 시스템의 성능을 좌우하는 매우 중요한 과정으로 많은 경우에 육안 검사로 매개변수를 선택하여 추정한다. 이 과정은 매우 주관적이고 특히 대량의 데이터인 경우 지루한 작업을 동반하므로 좋은 분석 결과를 보장하기 어렵다. 이러한 이유로 기준선 보정에서 최적의 매개변수를 결정하기 위한 객관적인 방법이 필요하다. 제안한 결정함수는 기준선 보정에 사용 가능한 매개변수 범위의 중앙값이 신호의 길이가 길어질수록 증가하고, 신호의 차수가 작아질수록 감소하는 관계를 정리하여 모델링하였다. 모의실험 데이터는 신호의 길이 7가지에 대해 조합한 분석신호 4가지와 선형 기준선과 2차, 3차, 4차 곡선 기준선을 각각 더하여 모두 112개를 생성하였다. 모의실험 데이터와 실제 라만 분광신호를 이용한 실험에서 제안한 결정함수의 평활화 매개변수가 기준선 보정에 효과적으로 적용될 수 있음을 확인하였다.

Keywords

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Fig. 1. The Range and median of smoothing parameter by length and order of the signal

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Fig. 2. A analytic signal with 2 Gaussian peaks

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Fig. 3. Various baselines and analytic signals used for simulated signals

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Fig. 4. The Range, median of smoothing parameter and determined parameter by length of the signal with linear baseline

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Fig. 5. The Range, median of smoothing parameter and determined parameter by length of the signal with quadratic baseline

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Fig. 6. The Range, median of smoothing parameter and determined parameter by length of the signal with cubic baseline

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Fig. 7. The Range, median of smoothing parameter and determined parameter by length of the signal with 4th order baseline

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Fig. 8. The result of baseline correction of 3,5-DNT Raman spectrum by determined parameter using the proposed method

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Fig. 9. The result of baseline correction of 4-ADNT Raman spectrum by determined parameter using the proposed method

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Fig. 10. The result of baseline correction of ethanol Raman spectrum by determined parameter using the proposed method

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Fig. 11. The result of baseline correction of NTO Raman spectrum by determined parameter using the proposed method

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