In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical tree, which is assumed to capture the geometry and structure of the input data. It is applied to the data using a modified version of the common one-dimensional (1D) wavelet filtering and decimation scheme, which can employ different wavelet filters. In each level of this wavelet decomposition scheme, a permutation derived from the tree is applied to the approximation coefficients, before they are filtered. We propose a tree construction method that results in an efficient representation of the input function in the transform domain. We show that the proposed transform is more efficient than both the 1D and two-dimensional (2D) separable wavelet transforms in representing images. We also explore the application of the proposed transform to image denoising, and show that combined with a subimage averaging scheme, it achieves denoising results which are similar to those obtained with the K-SVD algorithm.
aiWave: Volumetric Image Compression with 3-D Trained Affine Wavelet-like Transform
University of Science and Technology of China（中国科学技术大学）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）
Adaptive compressed 3D imaging based on wavelet trees and Hadamard multiplexing with a single photon counting detector
Jiangsu Key Lab of Spectral Imaging & Intelligence Sense, Nanjing University of Science and Technology（南京理工大学江苏省光谱成像与智能感知重点实验室）；Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology（南京理工大学高维信息智能感知与系统教育部重点实验室）
WaveGuard: Robust Deepfake Detection and Source Tracing via Dual-Tree Complex Wavelet and Graph Neural Networks
College of Computer Science and Technology, Xinjiang University（新疆大学计算机科学与技术学院）；Xinjiang Multimodal Intelligent Processing and Information Security Engineering Technology Research Center（新疆多模态智能处理与信息安全工程技术研究中心）；College of Computer Science and Electronic Engineering, Hunan University（湖南大学计算机科学与电子工程学院）；School of Computer Science, Hefei University of Technology（合肥工业大学计算机科学与技术学院）
