基于有约束非负矩阵分解的原稿基色色料光谱预测方法

针对直接在光谱反射率空间，对原稿颜色样本光谱的主成分分析会导致特征向量的数目超过真实物理维度(原稿所用基色色料)的数量，以及特征向量和对应系数存在负值，不能直接表示原稿基色色料的光谱特性和对应浓度等情况。创新性的提出需根据原稿色料的光学特性建立一个完全线性的光谱空间，并在该空间中使用带约束条件的非负矩阵分解实现对原稿基色数量和光谱形状进行预测的方法。对此，首先设计了一个实现对原稿基色色料光谱预测方法的总体研究方案和实现步骤，再以透明色料原稿为例，研究如何选择和构建一个符合其光学特性的光谱线性空间，然后再在基本非负矩阵分解(BNMF)基础上提出针对基色色料光谱预测的有约束非负矩阵分解算法(SCNMF)。针对BNMF算法会出现多重最优解，为了提高预测精度，使矩阵分解结果有明确的物理意义，所提出的SCNMF算法需要满足4个约束条件：非负性约束;全加性约束;平滑性约束;稀疏性约束。建立了满足约束条件的目标函数和迭代算法。预测结果表明本文提出的新方法能有效的实现对原稿基色物理维度和基色色料光谱的准确预测。

The Spectral Prediction of Original Primary Pigment Based on Constrained Non-Negative Matrix Factorization

With direct prediction in the spectral reflectance space with principal component analysis,the numbers of eigenvectors will surpass the numbers of real primary pigments while the eigenvectors and the corresponding coefficients have negative value, which can not directly presented original primary pigment spectral characteristics and corresponding concentration.We proposed an innovative spectral prediction method in which a complete linear spectral space was created according to optical properties of originals pigment.A constrained non-negative matrix factorization algorithm to predict the numbers and spectral curve shapes of real primary pigments was used in the space.So,this paper designed an overall research plan and implementation process about spectral prediction method firstly,and studied how to select and establish a spectral linear space which was conformed to optical properties of originals;taking transparent pigments as example,and spectra constrained non-negative matrix factorization (SC-NMF)algorithm was established to predict primary pigment spectra based on basic non-negative matrix factorization algorithm (BNMF).Aiming at realizing multiple optimal solution of BNMF and improving the prediction accuracy as well as make the ma-trix decomposition results to be clearly physically meaningful;the proposed SCNMF needs to satisfy four constraints:non nega-tive constraint,additive constraint,smoothness constraint and sparseness constraint.The obj ective function and iterative algo-rithm to meet four constraints were set up.The prediction results show that the proposed method can realize accurate prediction of original primary pigments’numbers and spectra effectively.