希爾伯特-黃變換在二維數據分析上之應用

The application of Hilbert-Huang Transform in two dimensional data analysis

張開維(Kai-Wei Zhang)

指導教授 ： 張建中 ； 蕭述三

國立中央大學/工學院/機械工程學系/碩士(2011年)

摘要

本文探討希爾伯特-黃轉換在二維數據及影像上的應用。傅立葉分析法為最常用之數據分析方法，但其限制在於難以求得局部頻譜性質。希爾伯特轉換法雖可求得瞬時頻率，但在合成訊號的應用上會得到錯誤的結果。希爾伯特-黃轉換中的經驗模態分解法能將合成訊號分解成單成份訊號，此時再使用希爾伯特轉換即可求得正確瞬時頻率。近年來，新發展之多維系綜經驗模態分解法能處理二維以上之數據影像資料。本研究應用一維及二維之經驗模態分解法，將分解後之各單元成份影像進行希爾伯特轉換，將其衍生的振幅譜、相位譜與頻率譜，配合以灰階分佈為基礎的熵值估算，進行不同結構影像資料的差異分析，實驗結果顯示多維系綜經驗模態分解法的確唯一良好的影像分析工具。

關鍵字

傅立葉分析法 ； 經驗模態分解法 ； 希爾伯特-黃轉換

並列摘要

This study focused on the application of Hilbert-Huang transform on two dimensional data and image. Fourier analysis is the most widely used data analysis method, but is limited in getting local frequency property. Hilbert Transform could be used to calculate instantaneous frequency, but is limited when applying on compound signals.
Empirical mode decomposition, part of the Hilbert-Huang transform, decompose multiple component signals to sum of single component signals, can lead to correct instantaneous frequency with Hilbert transform. The recent advances of multiple dimensional ensemble empirical mode decomposition could be applied on high dimensional data and image.
In this study, we first apply one- and two- dimensional empirical mode decomposition on a set of test image with different pattern feature. Then the histogram based entropy is calculated on the amplitude, phase and frequency image for the purpose of feature analysis. The results showed that multiple dimensional ensemble empirical mode decomposition is a well-performed data analysis tool.

並列關鍵字

Hilbert Hung transform ； Fourier analysis ； empirical mode

參考文獻

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