In this work, we propose a novel method for denoising unpaired low-dose computed tomography (CT) images using a cycle-consistent generative adversarial network (CycleGAN) model trained on wavelet sub-band images. A primary goal of CT imaging research is to reduce the amount of X-ray radiation exposure during a scan. However, CT image quality deteriorates with reduced radiation doses, making accurate diagnosis difficult. Denoising algorithms are necessary to reduce the X-ray dose while maintaining adequate visual quality. Deep learning methods, especially convolutional neural networks (CNNs), have recently come to prominence due to their superior performance and much faster inference times compared to previous medical image reconstruction techniques. However, supervised learning is challenging for CT because acquiring paired scans with different doses would expose patients to unnecessary radiation. Unpaired CT scans of different dosages can, however, be used for unsupervised learning. However, we find that naïve image domain learning produces mean shifting artifacts, especially in air filled regions. Thus, we use wavelet sub-band images, which have had low-frequency structural information removed from them via the wavelet transform, as CycleGAN inputs. The CycleGAN translates the wavelet sub-band images from low-dose images to high-dose images. Cycle consistency preserves the remaining structural information. Our method thereby allows the neural network to focus on learning how to alter the noise distribution. Moreover, it further prevents the model from introducing structural artifacts. We evaluate our method through extensive experimentation on temporal CT scans acquired in clinical settings.