Study on the Robust Wavelet Threshold Technique for Heavy-tailed Noises

Interesting signals are often contaminated by heavy-tailed noise that has more outliers than Gaussian noise. Under the introduction of probability model for heavy-tailed noises, a robust wavelet threshold based on the minimax description length principle is derived in the econtaminated normal family for maximizing the entropy. The performance and their measurement criterion for the robust wavelet threshold are studied in this paper. By the proposed performance measurement criterion, several kinds of noisy signals are processed with the wavelet thresholding techniques. Compared with classical threshold based on Gaussian assumption, the robust threshold can eliminate the heavy-tailed noise better, even if the precise value of epsilon is unknown, which shows its robustness. The further experiment shows that soft threshold is more suitable than hard threshold for robust wavelet threshold technique. Finally, the robust threshold technique is applied to denoise the practically measured gas sensor dynamic signals. Results show its good performances.