基于改进R矩阵方法的光谱反射率重建研究

王可; 王慧琴; 王展; 张毅; 殷颖

doi:10.3788/YJYXS20183304.0338

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基于改进R矩阵方法的光谱反射率重建研究

图像处理 | 更新时间：2020-07-06

- 基于改进R矩阵方法的光谱反射率重建研究
- Spectral reflectance reconstruction based on improved matrix R method
- 液晶与显示 2018年33卷第4期页码：338-346
- 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：
  
  [ "王可(1981-), 男, 山东荣成人, 博士研究生, 讲师, 2007年于西南交通大学获得硕士学位, 主要从事光谱图像处理及机器学习方面的研究。E-mail:wangke@xauat.edu.cn" ]
- 基金信息：
  
  国家自然科学基金青年基金(61701388);住建部科学技术计划资助项目(2017-K2-014);陕西省科技厅国际合作资助项目(2017KW-036);西安市科技局软科学资助项目(2016043SF/RK06（3）);西安市碑林区科技计划资助项目(GX1606);西安建筑科技大学青年基金(QN1628);西安建筑科技大学青年基金(QN1020);the Youth Fund of National Natural Science Foundation of China(61701388);Science and Technology Project of Ministry of Housing and Urban-Rural Development of China(2017-K2-014);International Science and Technology Cooperation Project of Science and Technology Department of Shaanxi Province, China(2017KW-036);Soft Science Project of Science and Technology Bureau of Xi'an, China(2016043SF/RK06(3));Science and Technology Project of Science and Technology Bureau of Xi'an Beilin District, China(GX1606);Youth Science and Technology Fund Project of Xi'an University of Architecture And Technology, China(QN1628);Youth Science and Technology Fund Project of Xi'an University of Architecture And Technology, China(QN1020)
- DOI：10.3788/YJYXS20183304.0338
  中图分类号： O433.4
- 收稿日期：2017-10-29，
  
  录用日期：2018-1-26，
  
  纸质出版日期：2018-04-05
- 稿件说明：
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王可, 王慧琴, 王展, 等. 基于改进R矩阵方法的光谱反射率重建研究[J]. 液晶与显示, 2018,33(4):338-346.

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.
王可, 王慧琴, 王展, 等. 基于改进R矩阵方法的光谱反射率重建研究[J]. 液晶与显示, 2018,33(4):338-346. DOI： 10.3788/YJYXS20183304.0338.

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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