印刷品原色油墨光谱预测中减色线性经验空间的建立

The Spectral Prediction Method of Primary Ink for Prints Manuscript Based on Non-Negative Matrix Factorization

在半色调印刷品原色油墨光谱预测技术中,在原光谱反射率空间进行主成分分析得到的代表性基向量数目会大于实际所使用的原色油墨数目,即光谱反射率空间并不适用光谱预测,且主成分分析得到的基向量会出现负值,没有物理意义。针对上述问题,建立了一个减色线性经验空间模型及其空间转换模型,并探究了影响经验空间线性程度n值的因素,通过实验及优化算法创新性找到确定最佳n值的方法,并在该减色线性经验空间进行半色调原稿原色油墨的预测实验。实验结果表明,在不同n值下,选取原始光谱反射率R_m和重构光谱反射率R_(recon)的f范数平方值的最小值对应的n值做为建立线性经验空间确定最佳n值的方法是有效的;为了将纸张和油墨类型对空间转换因数n的影响程度减到最小,最终确定n值为3.5;在减色线性经验空间进行印刷品原色油墨数目预测,得到的代表性基向量数目恰好等于实际印刷使用的原色油墨数目4,进行原色油墨光谱预测,预测的4色油墨除K色外,其他CMY色与实际原色油墨光谱相比拟合度GFC均大于99.9%。即所提出的优化n值的新方法建立的减色线性经验空间是一个可作为半色调印刷品原色油墨数目预测和光谱预测的有效线性空间。

In the spectral prediction technology of the primary ink of halftone prints manuscript, the representative vector number obtained by principal component analysis will be greater than the actual number of primary inks used in the reflectance space. The space is not suitable for spectral prediction, and the based vectors obtained by PCA will appear negative. There is no physical meaning. Aiming at the above problems, a subtractive linear experimental space model and space conversion model were created. And the factors influencing the linearity degree of the space n value were explored. Through experiments and optimization algorithms, the methods for determining the best n value were found innovatively. Then the prediction experiments of the primary ink of halftone prints manuscript were carried out in the space. The experimental results showed that, under different n values, the n value corresponding to the minimum square value of the f norm was effective for determining the best n value to establishing the linear empirical space. Finally, the n value was determined to be 3.5. In the space, the number of representative base vectors obtained by the method of number prediction was exactly equal to 4, which was the actual primary ink number. In spectral prediction, in addition to K color, other CMY color compared to the actual primary ink spectrum, the fitting degree of GFC was greater than 99.9%. That was to establish a new method for the optimization of n proposed in this paper. The value of color space was an effective linear empirical linear space which can be used as a halftone color ink number prediction and spectral prediction. That is to say, the space created by the new method is an effective linear space that can be used to predict the number of primary ink and the spectrum of halftone prints manuscript.