Spectral reflectance reconstruction based on improved matrix R method

Ke WANG; Hui-qin WANG; Zhan WANG; Yi ZHANG; Ying YIN

doi:10.3788/YJYXS20183304.0338

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Spectral reflectance reconstruction based on improved matrix R method

Image Processing | 更新时间：2020-07-06

- Spectral reflectance reconstruction based on improved matrix R method
- Chinese Journal of Liquid Crystals and Displays Vol. 33, Issue 4, Pages: 338-346(2018)
- 作者机构：
  
  1.西安建筑科技大学管理学院, 陕西西安 710055
  2.西安建筑科技大学信息与控制工程学院, 陕西西安 710055
  3.陕西省文物保护研究院, 陕西西安 710075
- 作者简介：
- 基金信息：
- DOI：10.3788/YJYXS20183304.0338
  CLC： O433.4
- Received：29 October 2017，
  
  Accepted：26 January 2018，
  
  Published：05 April 2018
- 稿件说明：
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Ke WANG, Hui-qin WANG, Zhan WANG, et al. Spectral reflectance reconstruction based on improved matrix R method[J]. Chinese journal of liquid crystals and displays, 2018, 33(4): 338-346.
DOI：

Ke WANG, Hui-qin WANG, Zhan WANG, et al. Spectral reflectance reconstruction based on improved matrix R method[J]. Chinese journal of liquid crystals and displays, 2018, 33(4): 338-346. DOI： 10.3788/YJYXS20183304.0338.

摘要

为了解决传统R矩阵方法重建光谱反射率过程中的病态问题，提出了一种正则化R矩阵改进方法。研究了如何使用Tikhonov正则化来限制R矩阵方法求解Moore-Penrose伪逆矩阵中所产生的病态问题，同时使用L曲线方法从训练样本数据中得到有效限制病态情况的最优正则化参数。实验结果表明：与R矩阵方法相比，改进的正则化R矩阵方法重建的光谱精度的平均均方根误差值降低了0.004 25，平均适应度系数值提高了1.325%，色度精度的平均色差值降低了0.141 9，并且在实际的应用中具有较好的表现。该方法能够满足精度较高的文物艺术品颜色再现的需要。

Abstract

In order to solve the ill-posed problem in the process of reconstructing the spectral reflectance using the traditional matrix R method

an improved matrix R method was proposed in this paper. The Tikhonov regularization method was researched to restrict the ill-posed problem to solve the Moore-Penrose pseudo inverse matrix. The L-curve method was used to obtain the optimal regularization parameter by training samples data in order to effectively restrict the ill-posed situation. The experimental results verified that compared with traditional matrix R method

the proposed regularization matrix R method had higher spectral and chromatic accuracy of reconstructed spectrum whose mean root mean square error value reduced 0.004 25

mean goodness of fit coefficient value improved 1.325%

and mean color difference value reduced 0.141 9. At the same time

the proposed regularization matrix R method achieved good performance in practical application. It can meet the high accuracy of cultural relics color reproduction needs.

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references

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