Robust Time Series Denoising with Learnable Wavelet Packet Transform

In many applications, signal denoising is often the first pre-processing step before any subsequent analysis or learning task. In this paper, we propose to apply a deep learning denoising model inspired by a signal processing, a learnable version of wavelet packet transform. The proposed algorithm has signficant learning capabilities with few interpretable parameters and has an intuitive initialisation. We propose a post-learning modification of the parameters to adapt the denoising to different noise levels. We evaluate the performance of the proposed methodology on two case studies and compare it to other state of the art approaches, including wavelet schrinkage denoising, convolutional neural network, autoencoder and U-net deep models. The first case study is based on designed functions that have typically been used to study denoising properties of the algorithms. The second case study is an audio background removal task. We demonstrate how the proposed algorithm relates to the universality of signal processing methods and the learning capabilities of deep learning approaches. In particular, we evaluate the obtained denoising performances on structured noisy signals inside and outside the classes used for training. In addition to having good performance in denoising signals inside and outside to the training class, our method shows to be particularly robust when different noise levels, noise types and artifacts are added.