X-ray Computed Tomography (CT) scans, while useful, emit harmful radiation which is why low-dose image acquisition is desired. However, noise corruption in these cases is a difficult obstacle. CT image denoising is a challenging topic because of the difficulty in modeling noise. In this study, we propose taking an image decomposition approach to removing noise from low-dose CT images. We model the image as the superposition of a structure layer and a noise layer. Total Variation (TV) minimization is used to learn two dictionaries to represent each layer independently, and sparse coding is used to separate them. Finally, an iterative post-processing stage is introduced that uses image-adapted curvelet dictionaries to recover blurred edges. Our results demonstrate that image separation is a viable alternative to the classic K-SVD denoising method.