Robust time series denoising with learnable wavelet packet transform

Noise in the data is one of the main cause of model performance drop. Denoising is therefore a critical step in most data pipelines. In this paper we propose to fuse the learning abilities of Neural Network with the well-proven efficiency of the wavelet packet shrinkage denoising method. Our deep convolutional neural network is designed to learn the wavelet and denoising parameters of the wavelet packet shrinkage and provides the following advantage compared to existing literature: (1) It outperforms state-of-the-art approaches in two denoising tasks, a synthetical task, where we can highlight the denoising abilities of the approach and a background noise removal task from a real dataset. (2) It has a very limited number of parameters to learn, up to 100x less than an equivalent CNN; (3) it is therefore much less prone to overfitting. (4) It generalizes extremely well to new noise levels as the denoising parameters can be easily modified without any fine-tuning required. Overall, our experiments show that our network is an efficient signal processing tool that learns a universal signal representation: its initialization is intuitive and it has strong learning capabilities making it much easier to implement than many other denoising approaches.