Removing specular reflections from images is critical for improving the performance of computer vision algorithms. Recently, state-of-the-art methods have demonstrated remarkably good performance at removing specular reflections from chromatic images. These methods are typically based on the chromatic pixels assumption; therefore, they are prone to failure in the achromatic regions. This paper presents a novel method that is applicable to natural images, because it is effective for both chromatic and achromatic regions. The proposed method is based on modeling the general properties of diffuse and specular reflections in a solid convex optimization framework. Considering the physical constraints, we determine the global optimal solution using the split Bregman method. Experimental results demonstrate the effectiveness of the proposed method, particularly for the achromatic regions, and its competence as a state-of-the-art method for removing specular reflections from the chromatic regions.