将经验小波变换拓展至二维图像，自适应构建小波、脊波和曲线波框架。
2D Empirical Transforms. Wavelets, Ridgelets and Curvelets revisited
- 基于信号自适应构造二维小波、脊波与曲线波基函数
- 新框架在图像分析中展现出优于传统方法的性能
- 适合图像去噪、边缘检测等需要自适应局部特征的场景
最近提出的「经验小波变换」方法旨在根据待分析信号构建一维自适应小波框架。本文将该方法拓展至二维信号（图像），重新审视了若干经典变换（张量小波、Littlewood-Paley小波、脊波和曲线波），并证明可构建其经验对应版本。这些构造生成了具有不同自适应特性的新框架，在图像分析与处理中表现出良好潜力。
原文摘要 · Abstract (English)
A recently developed new approach, called ``Empirical Wavelet Transform'', aims to build 1D adaptive wavelet frames accordingly to the analyzed signal. In this paper, we present several extensions of this approach to 2D signals (images). We revisit some well-known transforms (tensor wavelets, Littlewood-Paley wavelets, ridgelets and curvelets) and show that it is possible to build their empirical counterpart. We prove that such constructions lead to different adaptive frames which show some promising properties for image analysis and processing.
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