Noise reduction is an important preprocessing step for many visualization techniques that make use of feature extraction. We propose a method for denoising 2-D vector fields that are corrupted by additive noise. The method is based on the vector wavelet transform and wavelet coefficient thresholding. We compare our wavelet-based denoising method with Gaussian filtering, and test the effect of these methods on the signal-to-noise ratio (SNR) of the vector fields before and after denoising. We also study the effect on relevant details for visualization, such as vortex measures. The results show that for low SNR, Gaussian filtering with large kernels has a somewhat higher performance than the wavelet-based method in terms of SNR. For larger SNR, the wavelet-based method outperforms Gaussian filtering. This is mostly due to the fact that Gaussian filtering tends to remove small details, which are preserved by the wavelet-based method.