tfShearlab：用于深度学习的TensorFlow数字剪切波变换
tfShearlab: The TensorFlow Digital Shearlet Transform for Deep Learning
摘要：
应用谐波分析的剪切波变换是目前分析具有各向异性奇异性的多维信号的最新技术。它的最佳稀疏近似特性和其忠实的数字化允许剪切波被应用到不同的问题，从成像科学，如图像去噪，图像修复和奇异点检测。剪切波变换也被成功地利用，例如，作为特征提取器。因此，它已被证明非常适合与数据驱动方法（如深度神经网络）相结合的图像预处理。这特别需要在当前的深度学习框架（如TensorFlow）中实现shearlet变换。出于这个动机，我们开发了一个张量剪切波变换，旨在提供一个忠实的TensorFlow实现。除了在预测模型中的可用性外，我们还观察到变换性能的显着改善，运行时间几乎是以前最先进实现的40倍。在本文中，我们还将介绍几个数值实验，如图像去噪和修复，其中TensorFlow版本可以显示出优于以前的库以及学习的原始-对偶重建方法，用于低剂量计算机断层扫描在运行时间。
英文摘要：
The shearlet transform from applied harmonic analysis is currently the state of the art when analyzing multidimensional signals with anisotropic singularities. Its optimal sparse approximation properties and its faithful digitalization allow shearlets to be applied to different problems from imaging science, such as image denoising, image inpainting, and singularities detection. The shearlet transform has also be successfully utilized, for instance, as a feature extractor. As such it has been shown to be well suited for image preprocessing in combination with data-driven methods such as deep neural networks. This requires in particular an implementation of the shearlet transform in the current deep learning frameworks, such as TensorFlow. With this motivation we developed a tensor shearlet transform aiming to provide a faithful TensorFlow implementation. In addition to its usability in predictive models, we also observed an significant improvement in the performance of the transform, with a running time of almost 40 times the previous state-of-the-art implementation. In this paper, we will also present several numerical experiments such as image denoising and inpainting, where the TensorFlow version can be shown to outperform previous libraries as well as the learned primal-dual reconstruction method for low dose computed tomography in running time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
