Denoising is an important application of image processing, especially for medical image data. These images tend to be very noisy when a low radiation dose, less harmful to the patient, is used for acquisition. For computed tomography (CT) data, it is possible to simulate realistic low dose images from the raw scanner data. We use this data to construct a supervised denoising system, that learns an optimal mapping from input features to denoised voxel values. As input features we use several general filters and the output of existing standard noise reduction filters, notably non-linear diffusion schemes. After feature selection, these are mapped to the denoised values by k-nearest neighbor and support vector regression. The resulting regression denoising systems are shown to perform significantly better than non-linear diffusion schemes, Gaussian smoothing and median filtering in experiments on CT chest scans.