本論文提出的快速二維經驗模態分解法，係結合均值濾波、快速卷積及基於提洛涅三角化方法之次序統計濾波器窗口決定法等三種演算法，對經驗模態分解法內的過篩程序自各層面達到加速效果。在包絡插補上，基於過去文獻之探討而提出改良的均值濾波器方法，直接插補出均值包絡，並針對線性卷積這項特性，以奇異值分解方式降低卷積運算的運行時間。文中提出的濾波器結合了次序統計濾波器，並以提洛涅三角化方法改進在決定濾波器窗口大小時，因需計算大量歐幾里德距離而產生的耗時問題。最後，實驗結果顯示此論文之方法較過去文獻更能快速地分解出高品質的本質模態函數。

In this thesis, a mean approach is proposed for the acceleration of the bidimensional empirical mode decomposition (BEMD). In the envelope generation process, the proposed method uses a modified mean filter to approximate the interpolated envelope of conventional BEMD, and utilizes a convolution algorithm based on singular value decomposition (SVD) to further reduce the computation time. Order statistics filter width determination, originally used in the fast and adaptive bidimensional empirical mode decomposition (FABEMD), is applied to adaptively formulate an envelope. Considering the computation efficiency, the proposed method improves the algorithm for calculating distances among extrema by using Delaunay triangulation (DT). The experimental results show that the mean approach can produce intrinsic mode functions faster than FABEMD , while retaining acceptable quality.

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