A color image is the result of a very complex physical process. This process involves both light reflectance due to the surface of the object and the sensor. The sensor is the human eye or the image acquisition system. To avoid metamerism phenomena and to give better rendering to the color images resulting from the synthesis, it is sometimes necessary to work in the spectral field. Now, we meet two classes of methods that enable the closest spectral image to be produced from color images. The first method uses circular and exponential functions. The second method uses the Penrose inverse or the Wiener inverse. In this article, we first of all describe the two methods used in a variety of fields from image synthesis to colorimetry not to forget satellite imagery. We then propose a new method linked with the neural network so as to improve the first two approximation methods. This new method can also be used for calibrating most of color digitization systems and sub wavelengths color array filters.