The time-frequency analysis for image signal is one of the significant and difficult domains in image processing technology. The aim of it is to analysis how the frequency components vary in local time or local space and utilize the time-frequency features, such as instantaneous frequency, to accomplish image processing assignments. The tools and algorithms for image time-frequency analysis are just researched in this thesis. This thesis researches EMD and quaternionic spectrum analysis deeply, which are novel time-frequency analysis tools, and achieves actual evolve in image analysis. At first, the 2-D separable EMD based on the characters of 1-D EMD is introduced in this thesis, which extends the 1-D EMD to 2-D; Then, in order to analysis analytic signal for 2-D signals, this thesis researches the quaternionic analytic signal and introduces a fast quaternionic Fourier transform and inverse quaternionic Fourier transform algorithm. Simultaneously, this thesis puts forward a novel phase definition for quaternionic analytic signal, which overcomes some shortcomings of the exist definition. In the application domain of image time-frequency analysis, this thesis also does some research. First, an unsupervised texture segmentation algorithm is proposed in this thesis, based on the characters of 2-D separable EMD and quaternionic analytic signal; Second, this thesis introduces a novel texture compression method based on 2-D separable EMD; At last, it analysis texture Wold decomposition in quaternionic spectrum domain, based on fast quaternionic spectrum computing algorithm. Theory analysis and experiment results indicate that the algorithms proposed in this thesis have respective advantages, such as innovation, accuracy, simplicity, applicability, etc. This thesis explores a reasonable way to use EMD and quaternionic spectrum analysis in image analysis domain.
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