Multi-energy CT acquires simultaneous multiple x-ray attenuation measurements from different energy spectra which facilitates the computation of virtual monoenergetic images (VMI) at a specific photon energy (keV). Since the contrast between iodine attenuation and the attenuation of surrounding soft tissues increases at lower x-ray energies, VMIs in the range of 40-70 keV can be used to improve iodine visualization. However, at lower energy levels, image noise in VMIs is substantially increased, which counteracts the benefits from the increased iodine contrast, resulting in a decreased iodine contrast-to-noise ratio (CNR). There exists considerable data redundancy between multi-energy CT images created from the same acquisition. Similarly, a substantial spatio-spectral data redundancy exists between multi-energy CT images and the corresponding VMIs. In this work, we develop a denoising framework that exploits this data redundancy to improve iodine CNR in the VMIs. We accomplish this by applying prior-knowledge-aware iterative denoising to low-energy VMIs; we refer to the denoised images as mono-PKAID images. The proposed framework was evaluated using phantom and in vivo data acquired on a research whole-body photon-counting-detector CT, as well as using data from a commercial dual-source dual-energy CT system. The results of phantom experiments show that the proposed framework can preserve image resolution and noise texture compared to the original VMIs, while reducing noise to improve iodine CNR. Quantitative measurements show that the iodine CNR of 50 keV VMI is improved by 1.8-fold using the proposed method, relative to the VMI produced using commercial software (Mono+). With mono-PKAID, VMIs at lower keV take full advantage of higher iodine contrast without substantially increasing image noise. These observations were confirmed using patient data sets, which demonstrated that mono-PKAID reduced image noise, improved CNR in anatomical regions with iodine perfusion by 1.8-fold, and potentially enhanced the visibility of focal liver lesions.