基于解析法和谱图法的二维瞬时频率分析

Traditional methods of time-frequency analysis are based on linear and stationary assumptions. However, the data, no matter natural or man-made, usually are nonlinear and non-stationary, which leads to the failure of traditional time-frequency methods. Instantaneous frequency is a necessary quantity for the comprehensive understanding of the detailed mechanisms in nonlinear and non-stationary processes as functions of time that give sharp identifications of imbedded structures. Two-dimensional instantaneous frequency based on the local properties of the signal offers an intrinsic character of nonlinear and non-stationary signals. .This project aims at offering a reasonable definition of two-dimensional instantaneous frequency using analytic signal and spectrum method.The main content includes: .Two-dimensional Hilbert transform is analyzed, from which two dimensional analytic signal is got for obtaining the two-dimensional instantaneous frequency. Two-dimensional instantaneous frequency is aslo deduced from the spectrum method. In addition, the definition of two-dimensional instantaneous frequency is validated by the standard narrow band signal and the physical meaning of two-dimensional instantaneous frequency is checked. Reasonable two-dimensional instantaneous frequency is developed. Finally, a new decomposition method is constructed by the two-dimensional instantaneous frequency after defining the narrow band signal. The decomposition method based on the characters of the signal is an adaptive method. The proposed research provides significant approaches in texture analysis and processing. The underlying patterns and the intrinsic information of image are revealed by the two-dimensional instantaneous frequency..This project forms the basis for a general theory of image processing and has a considerable prospect in character extracting, image classifying and related areas. As a generalized method for time-frequency analysis of two-dimensional non-stationary signals, this project is not only meaningful for analyzing and exploiting nonlinear signals, but also reveals their profound physical frequency characters.

传统的时频分析方法大多以平稳信号为前提展开研究，而现实中存在大量频率随时间变化的非线性、非平稳信号；此时，传统的时频分析方法不能有效、真实地展现非平稳信号的瞬时特征。因此，研究非线性、非平稳信号的瞬时频率特征是探索其内部蕴含特性的有效途径。二维瞬时频率是我们认知二维信号瞬时特征的重要手段。本项目从经典的解析法和谱图法入手，尝试定义二维瞬时频率及其合理表达，探寻一种能反映二维非平稳信号内在特征的新方法。主要研究内容包括：（1）设计合理的二维Hilbert变换方法，进而构造二维解析信号得到二维瞬时频率，并寻求一个基于谱图的频率提取方法；（2）利用二维瞬时频率分析二维信号，定义窄带信号，探求基于图像内部特征的分解算法，同时分析二维经验模式分解的特质。.二维瞬时频率分析为图像处理提供了新思路。作为时频分析方法的延伸和推广，项目成果有助于非线性科学中的纹理图像的解析,并揭示了信号的物理频率特征。

传统的时频分析方法大多以平稳信号为前提展开研究，而现实中存在大量频率随时间变化的非线性、非平稳信号；此时，传统的时频分析方法不能有效、真实地展现非平稳信号的瞬时特征。因此，研究非线性、非平稳信号的瞬时频率特征是探索其内部蕴含特性的有效途径。二维瞬时频率是我们认知二维信号瞬时特征的重要手段。本项目从经典的解析法和谱图法入手，尝试定义二维瞬时频率，提出一种能反映二维非平稳信号内在特征的新方法。主要研究内容包括：（1）研究合理的二维Hilbert变换方法，进而构造二维解析信号得到二维瞬时频率；（2）研究了基于二维经验模式分解和Monogenic解析信号的二维瞬时频率提取方法，成功提取了图像的二维振幅特征、二维瞬时频率等二维谱特征。振幅表示为局部信号的能量特征；相位表示图像局部的变化和结构，对相位求导会得到二维瞬时频率，二维瞬时频率可以反映图像独特的细节信息；（3）研究了基于多尺度单演解析信号提取的二维振幅的方法。振幅特征可以抑制杂波和直达波，我们利用此方法实现了探地雷达目标定位。（4）研究基于Shearlet变换和Monogenic相结合的方法提取了图像多方向多尺度的二维瞬时频率特征；使得每个Shearlet变换成分都有振幅、相位和频率特征；作为时频分析方法的延伸和推广，项目成果有助于非线性科学中的纹理图像的解析,并揭示了信号的物理频率特征。