The quality of a computed tomography (CT) image is often degraded by streaking artifacts resulting from excessive x-ray quantum noise. Often, a patient has to be rescanned at a higher technique or at a larger slice thickness in order to obtain an acceptable image for diagnosis. This results in a higher dose to the patient, a degraded cross plane resolution, or a reduced patient throughput. In this paper, we propose an adaptive filtering approach in Radon space based on the local statistical properties of the CT projections. We first model the noise characteristics of a projection sample undergoing important preprocessing steps. A filter is then designed such that its parameters are dynamically adjusted to adapt to the local noise characteristics. Because of the adaptive nature of the filter, a proper balance between streak artifact suppression and spatial resolution preservation is achieved. Phantom and clinical studies have been conducted to evaluate the robustness of our approach. Results demonstrate that the adaptive filtering approach is effective in reducing or eliminating quantum noise induced artifacts in CT. At the same time, the impact on the spatial resolution is kept at a low level.