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。

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.

Boashash B (2003) Time Frequency Analysis. Elsevier Chandran V, Carswell B, Boashash B, and Elgar S (1997) Pattern recognition using invariants defined from higher order spectra: 2-D image inputs. IEEE Transactions on Image Processing 6, 703-712.
Cohen L (1994) Time Frequency Analysis: Theory and Applications. Prentice Hall
Damerval C, Meignen S, and Perrier V (2005) A fast algorithm for bidimensional EMD. IEEE Signal Processing Letters 12, 701-704.
Flandrin P (1999) Time-frequency/time scale analysis. Academic Press,
Hahn SL (1996) Hilbert Transforms in Signal Processing. Artech House, Boston.
Huang NE and Attoh-Okine N (2005) The Hilbert-Huang Transform in Engineering. Taylor and Francis.
Huang NE and Shen SSP (2005) Hilbert-Huang Transform and its applications. World Scientific.
Huang NE, Shen Z, Long SR, Wu MLC, Shih HH, Zheng QN, Yen NC, Tung CC, and Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of The Royal Society of London Series A-Mathematical Physical and Engineering Sciences 454 (1971): 903-995.
Huang NE, Shen Z, Long SR (1999) A new view of nonlinear water waves: The Hilbert spectrum. Annual Review Of Fluid Mechanics 31 417-457.
Huang NE and Wu ZH (2008) A review on Hilbert-Huang transform: method and its applications to geophysical studies. Reviews of Geophysics 46, RG2006.
Ionescu R, Llobet E (2002) Wavelet transform-based fast feature extraction from temperature modulated semiconductor gas sensors. Sensors and Actuators B-Chemical 81, 289-295
Khan JF, Barner K, Adhami, R (2008) Feature point detection utilizing the empirical mode decomposition. EURASIP Journal on Advances in Signal Processing. 287061
Linderhed A (2005) Variable sampling of the empirical mode decomposition of two-dimensional signals. International Journal of Wavelets Multiresolution and Information Processing 3, 435-452.
Murtagh F, Starck JL (2008) Wavelet and curvelet moments for image classification: Application to aggregate mixture grading. Pattern Recognition Letters 29, 1557-1564.
Nunes JC, Bouaoune Y, Delechelle E, Niang O, and Bunel P (2003) Image analysis by bidimensional empirical mode decomposition. Image and Vision Computing 21, 1019-1026.
Nunes J, Guyot S, and Delechelle E (2005) Texture analysis based on local analysis of the bidimensional empirical mode decomposition. Machine Vision and Applications 16, 177-188.
Shao Y and Celenk M (2001) Higher-order spectra (HOS) invariants for shape recognition. Pattern Recognition 34, 2097-2113.
Tenllado C, Setoain J, Prieto M, Pinuel L, and Tirado F (2008) Parallel implementation of the 2D discrete wavelet transform on Graphics Processing Units: Filter Bank versus Lifting. IEEE Transactions on Parallel and Distributed Systems 19, 299-310.
Wu ZH and Huang NE (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method. Advances in Adaptive Data Analysis 1, 1-41.
Wu ZH, Huang NE and Chen XY (2009) The multi-dimensional ensemble empirical mode decomposition method. Advances in Adaptive Data Analysis 3, 339-372.
Wu ZH, Huang NE, Long SR, and Peng CK (2007) On the trend, detrending, and variability of nonlinear and nonstationary time series. Proceedings of The National Academy of Sciences of The United States of America 104, 14889-14894.
江宜鍵, 2006, “MPEG-4進階音響解碼器之實現與HHT於音響編碼之應用”, 成功大學
陳惠芳, 2003, “以希伯特黃轉換分析脊髓損傷病患起坐性暈眩之心率變異度”, 中原大學
翁海馨, 2008, “應用希爾伯特-黃轉換(HHT)法在晚第四紀赤道太平洋氣候之時間序列分析”, 海洋大學
黃國豪,2009, “應用希爾伯特黃變換(HHT)之邊際譜分析於旋轉機械的元件鬆脫故障診斷” ,中央大學
許寶琮, 2006,“短時頻分析於表面波譜法應用之初步探討”, 成功大學
湛翔智, 2002,“活塞式造波機模擬進岸碎玻氣泡之聲學分析”, 中山大學