Spectral reflectance recovery from a white-balanced RGB image based on the algorithm of compressive sensing

Abstract

In this work we study the methods for reconstructing spectral reflectances of images. To reproduce the spectral reflectance more accurately and the colours more realistically, we obtain a so-called average transformation matrix, using a series of different modulated light sources to illuminate a standard whiteboard. For eliminating the influence of those light sources on RGB images, we first use a white-balance algorithm to standardize the scene information, thus obtaining a uniform RGB image with different sources. Then we map the RGB image onto the spectral reflectance basing on a compressive sensing algorithm and the principal component analysis and, finally, reconstruct the spectral reflectance of the testing sample. We compare the reconstruction accuracies of our compressive sensing algorithm based on white-balance calibration with the results derived using a pseudo-inverse method and a traditional compressive sensing algorithm. Our simulation results show that, under the same conditions of reconstruction, the residual errors and the colour difference resulting from our improved algorithm are less than those produced by the other two algorithms. In other words, the reconstruction algorithm suggested by us outperforms the other methods and can provide better performance of image colour reproduction.