Spectral imaging technology, capable of integrating images and spectra, is widely used and has developed rapidly in the fields of color imaging, cultural heritage, artwork research, etc. Traditional color replication technology uses related equipment for direct replication through RGB values, which is affected by the isochromatic spectrum and results in inaccurate color replication. For more accurate color reproduction, spectral reflectance can be used as a medium for color information transmission to ensure that the reproduced color is the same as the actual color. Spectral reflectance reconstruction is an important research topic in optics. Its purpose is to reconstruct the spectral reflectance of an object through the equipment-related RGB values obtained by various imaging equipment, which is independent of equipment and illumination. Some traditional reflectance reconstruction methods, such as the principal component analysis and the pseudo-inverse method, are still insufficient in accuracy. There are also some improved methods based on them. For instance, the reflectance reconstruction method using a single lighting image combined with the weighted pseudo-inverse method can reduce the collected lighting images, but the matching information between colors is less. Therefore, the requirements for experimental conditions become higher, and there may be a homochromatic phenomenon affecting the reconstruction accuracy. To reduce the complexity and cost of spectral reflectance reconstruction equipment and achieve more accurate reflectance reconstruction on the wideband spectra, this study improves the principal component analysis and reconstructs spectral reflectance by combining the weighting coefficient and error correction function.

In this paper, a wideband multispectral imaging method is adopted. The red, green, and blue light of a projector is used as the light source to illuminate the surface of an object, and the spectral images are sampled by a color digital camera. According to the Euclidean distance relation, the experimental samples are sorted, and the 31 samples most relevant to the test samples are selected as the locally optimal training samples. The weight factor is added on the basis of the principal component analysis, and an error correction item is introduced according to the pseudo-inverse method to correct the reflectance reconstructed by the weighted principal component analysis. The corrected reflectance is used as the final output. The improved method is used to reconstruct the reflectance of SG140 color cards, dyed paper, and oil painting surfaces to verify the accuracy.

The improved method, principal component analysis, and weighted pseudo-inverse method are employed to reconstruct the reflectance separately. The results show that the experimental method has improved the accuracy of the reflectance reconstruction to different degrees after comparison. According to the reflectance of the reconstructed four pieces of dyed paper (Fig. 7), three kinds of data representing the reconstruction accuracy (Table 2), and the reflectance of some points on the reconstructed oil painting surfaces (Fig. 9) and its accuracy data (Table 3), the reflectance reconstruction accuracy of the painting and oil painting surfaces can also meet the expected requirements. According to the root-mean-square error data on the reflectance of the reconstructed SG140 color cards (Fig. 10), the root-mean-square error of the method in this paper is 2.4995, and that of the principal component analysis is 4.5812, while that of the weighted pseudo-inverse method is 3.4851. The proposed method significantly improves the reflectance reconstruction accuracy upon the improvement in the principal component analysis.

In the experimental analysis, three indexes (root-mean-square error, fitting coefficient, and spectral matching skewness index) are used to characterize the reflectance reconstruction accuracy and measure the reconstruction effect. The comparison with the principal component analysis and weighted pseudo-inverse method shows that the spectral reflectance reconstruction accuracy of the method in this experiment increases by about 45% on the basis of the principal component analysis. The color difference of SG140 color cards reconstructed by the three methods is further calculated, and the average value of the color difference is also smaller than that of the method proposed in this paper. The Euclidean distance between the training sample and the test sample is used to select the locally optimal training sample. When the number of samples is large, the amount of computation will be increased, which is not suitable for the situation requiring rapid reflectivity reconstruction.