A spectral match ensures a colour match of two object colours for all observers across different illuminants. Developing a spectral based colour reproduction system requires a spectral analysis in which the spectral reflectance of each pixel must be known.This paper describes a method for estimating the surface reflectance values of objects in a scene (or image) under a given illuminant and sensors of a digital camera. This work is motivated by the work of van Trigt using the smoothness condition for recovering reflectance of a given set of CIE tristimulus values X,Y,Z corresponding to a particular illuminant. He used integration of the square of the first derivative of the reflectance function as the smoothness restriction, and the functional analysis approach to develop a method for recovering the reflectance values. In this work, by using numerical integration techniques, the smoothness constraint is replaced by the square of the two norm of a vector, which is the multiplication of the smooth operator matrix and the reflectance vector. The proposed method is to solve a constrained-least-square problem. The testing results showed that the current method performed consistently better than those from the basis functions were compared with those from the basis-functions.