Denoising 2-D Vector Fields by Vector Wavelet Thresholding

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, which transforms a vector input signal to wavelet coefficients that are also vectors. We introduce modifications to scalar wavelet coefficient thresholding for dealing with vector-valued coefficients. 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 compare our method with component-wise scalar wavelet thresholding. Furthermore, we use a vortex measure to study the performances of the methods for retaining relevant details for visualization. The results show that for very low SNR, Gaussian filtering with large kernels has a slightly better performance than the wavelet-based method in terms of SNR. For larger SNR, the wavelet-based method outperforms Gaussian filtering, because Gaussian filtering removes small details that are preserved by the wavelet-based method. Component-wise denoising has a lower performance than our method.