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.
翻译:波列变换是现代数据分析和信号处理的基石。 它的数学本质是不可忘却的变换, 能够从频率域的快速变换中辨别出慢模式。 这种逆向变换可以通过设计正常流模式来学习。 这种变换可以通过一个设计好的正常流模式来学习。 以一个通用的升动方案为混合层, 一个与降序相仿的因子脱位层, 以及不同层次的参数共享, 人们可以训练正常流, 在不同级别过滤高频元素, 从而将传统的线形波列变换扩展为可学习的非线性深层学习模式。 在本文中, 提出了一种构建这种变换的方式, 并同时对所学的变换进行数字分析 。 然后, 我们展示了模型在图像无损压缩中的能力, 显示它能够实现SOTA压缩分数, 同时取得一个小模型大小、 大量一般化能力和 处理高维数据的能力 。