图信号的小波滤波器组设计及其在碳氢化合物QSPR研究上的应用

图信号处理是非欧空间信息处理领域近年来兴起的一个新的研究方向，本项目将研究图信号小波滤波器组的设计及其在碳氢化合物结构性质定量关系（QSPR）研究上的应用。我们将摒弃现有对滤波器组的构造方法，采用直接构造离散数据点的分布并对其进行多项式拟合的方法实现图信号小波滤波器组的反向直接设计。在设计过程中重点解决图信号的下采样定义、各向异性扩散小波的设计等问题。我们将在图小波域的不同尺度下，研究碳氢化合物拓扑指数的定义，探索其分子结构与性质（沸点、稳定性等）之间新的定量关系。项目课题组已有丰富的相关研究积累，拟研究的问题创新性强，融合了信号处理、图像处理、最优化技术等多学科交叉技术与知识，无论是从图信号处理的理论研究角度，还是从分析碳氢化合物分子结构的实际应用角度来看，本项目都具有重要的科学意义和广泛的应用前景。

Graph signal processing is a hot research area of non-Euclidean signal processing in recent years. The main objective of this project is the design of graph wavelet filter bank and its application in hydrocarbon QSPR research. Abandoning common ideas, we will realize the reverse-direct design of graph wavelet filter bank in discrete domain, through constructing the distribution of discrete data and performing polynomial fitting for them. During the design, we will focus on solving some key problems, such as graph downsampling and the design of anisotropic diffusion wavelets. We will consider the definition of the hydrocarbon topological index and explore the new quantitative relationship between its molecular structure and properties (boiling point, stability, etc.) in the graph wavelet domain. The project team has good track record of research. The proposed research problems are highly innovative and range cross-disciplines such as signal processing, image processing, and optimal technique. The project is significant in both theoretical research as well as practical application, from the perspective of graph signal processing and the application of hydrocarbon molecular structure.