Learning Non-linear Wavelet Transformation via Normalizing Flow
This work addresses the need for more efficient and adaptable signal processing tools in data analysis, though it appears incremental by building on existing wavelet and normalizing flow techniques.
The paper tackles the problem of extending traditional linear wavelet transformations to learnable non-linear deep learning models using normalizing flow, achieving state-of-the-art compression scores in image lossless compression with a small model size and substantial generalization ability.
Wavelet transformation stands as a cornerstone in modern data analysis and signal processing. Its mathematical essence is an invertible transformation that discerns slow patterns from fast ones in the frequency domain. Such an invertible transformation can be learned by a designed normalizing flow model. With a generalized lifting scheme as coupling layers, a factor-out layer resembling the downsampling, and parameter sharing at different levels of the model, one can train the normalizing flow to filter high-frequency elements at different levels, thus extending traditional linear wavelet transformations to learnable non-linear deep learning models. In this paper, a way of building such flow is proposed, along with a numerical analysis of the learned transformation. Then, we demonstrate the model's ability in image lossless compression, show it can achieve SOTA compression scores while achieving a small model size, substantial generalization ability, and the ability to handle high-dimensional data.