Reconstruction of spectrum or spectral reflectance using only tristimulus values is impossible because of the infinite number of metamers. However, with additional information about the type of light source or surface, approximate reconstruction is possible. Several studies were written on this topic using Principal Component Analysis (PCA): using a sample set of spectra (or spectral reflectance) the search space for appropriate metamer can be narrowed. In this paper a new PCA-based optimization method is presented, which is more accurate than that of published before and gives non-negative, smooth results. Using precalculated lookup tables, the time and memory consumption will be very small. This method can produce a good reconstructed, realistic spectrum of an illuminant or spectral reflectance function for a surface based on tristimulus values of a digital image.