Denoising 2-D Vector Fields by Vector Wavelet Thresholding

Michel A. Westenberg and Thomas Ertl

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.