A Dual-Energy CT (DECT) with a spectral detector greatly extends the capabilities of CT by incorporating energy-dependent information of the X-ray attenuation. In order to fully exploit DECT capabilities, it is required to perform a process known as spectral decomposition. However, this process is sensitive to noise, suffers from reduced photon count per layer in DECT scans and generates anti-correlated noise in the estimated material specific images. In order to overcome these problems, the Anti-Correlated Rudin, Osher and Fatemi (AC-ROF) model is applied for noise reduction, exploiting the relationship between the material-specific images. However, this model deteriorates the structural information with intense noise. In this paper we propose to extend this method by integrating it into an iterative reconstruction procedure to improve the noise reduction performance. The resulting algorithm is called Iterative Reconstruction AC-ROF, or IR-AC-ROF. We have tested AC-ROF and IR-AC-ROF algorithms with realistic brain simulation phantoms and show encouraging results indicating that the resulting material-specific images of IR-AC-ROF can generate better mono-energetic images with improved brain structure visibility. This demonstrates the benefit of including the noise reduction constraints within the reconstruction procedure, rather than using them in a post-processing step.