光谱反射率描述物体的表面颜色特征, 为了能够获取物体自身更加精确的颜色信息, 在图像处理领域光谱反射率重构成为了关注的话题。 反射光谱重构算法是对实验物体表面在可见光范围内每一波长处的光谱反射率进行重构, 以达到提高物体自身颜色准确复制的精度, 最后建立相应的反射光谱。 尝试将压缩感知(CS)理论应用到光谱实验中, 对光谱反射率进行重构。 首先是介绍了压缩感知理论知识, 然后把压缩感知理论与光谱反射率原理相结合, 根据基于压缩感知的光谱反射率重构的理论框架, 选取合适的采样值, 压缩感知的采样值即压缩值, 小波基作为正交矩阵, 高斯随机矩阵作为测量矩阵, 正交矩阵与测量矩阵需要保证具有不相关性, 将原始光谱反射率从高维到低维进行线性投影, 得到低维的观测信号, 运行简单的正交匹配追踪算法(OMP)对低维的观测信号进行由低维到高维的高精度重构, 重构得到的光谱反射率与原始光谱反射率具有相同的维度, 最后将压缩感知重构算法与传统的光谱反射率重构算法伪逆法与多项式回归法进行比较。 经过压缩感知重构算法得到的色差值与均方根误差值都小于伪逆法和多项式回归法重构的结果, 经压缩感知的重构精度明显提高; 经压缩感知重构的光谱曲线可以达到或者更接近原始光谱曲线的峰值, 整体效果更接近原始光谱曲线; 经多项式回归法和伪逆法重构的光谱曲线达不到原始峰值, 整体上存在偏差。 可以认为压缩感知用低采样的数据达到了全采样的效果, 提高了光谱反射率重构的精度。 基于压缩感知的光谱反射率重构算法效果明显优于传统的多项式回归法和伪逆法, 可以将压缩感知理论应用到实际的多光谱成像系统中。

The spectral reflectance describes the surface color characteristics of the object. In order to obtain more accurate color information of the object, the spectral reflectance reconstruction in the image processing field has become a hot topic. We take the spectral reflectance as the main research target. Sequentially, we propose the algorithm which reconstructs the spectral reflectance of the measured object in the visible region to enhance the accuracy of color reproduction. This article attempts to employ compressed sensing (CS) theory in the spectral experiments to reconstruct the spectral reflectance. This article first introduces the theory of compressive sensing and then combines the theory of compressive sensing with the principle of spectral reflectance. According to the theoretical framework of spectral reflectance reconstruction based on compressed sensing. The appropriate sampling value is selected.The compressed sensing sample value is the compressed value, the wavelet base is used as the orthogonal matrix, and the Gaussian random matrix is used as the measurement matrix, the orthogonal matrix and the measurement matrix ensure irrelevance, the original spectral reflectance is linearly projected from the high dimension to the low dimension, then a low-dimensional observation signal is obtained, the simple orthogonal matching pursuit algorithm (OMP) reconstructs the low-dimensional to high-dimensional high-precision observation signals from low-dimensional observation signals, and the obtained spectral reflectance has the same dimensions as the original spectral reflectance. Finally, the compressed inverse method and the traditional spectral reflectance reconstruction algorithm are compared with thepseudo-inverse method and the polynomial regression method. The experimental results showthat the color difference and the root mean square error obtained by the compressed sensing reconstruction algorithm are smaller than the measured value of the pseudo-inverse method and the polynomial regression method, In other words, the reconstruction accuracy is significantly improved, the spectral curve reconstructed by compressed sensing can reach or be closer to the peak of the original spectral curve, which is closer to the original spectral curve on the whole visible range. The spectral curve reconstructed by the polynomial regression method and the pseudo-inverse method does not reach the original peak, and there is an overall deviation. Inconclusion, the experimental resultsshow that compressed sensing uses low-sampling data to achieve the effect of full sampling. Compressed sensing improves the accuracy of spectral reflectance reconstruction while reducing the amount of computation. The compression reconstruction effect proposed in this paper is significantly better than the traditional polynomial regression method and the pseudo-inverse method. Compressed sensing theory can be applied to practical multispectral imaging systems.