本研究提出一種基於多維均勻相位經驗模態分解（Multi-Dimensional Uniform Phase Empirical Mode Decomposition, Multi-Dimensional UPEMD）的影像分解方法，作為傳統多維總體經驗模態分解（MEEMD）的改良。該方法將 MEEMD 中的 EEMD 分解過程替換為 Uniform Phase EMD，透過加入具均勻相位分佈的窄頻正弦波進行相位遮罩，取代隨機白噪音擾動，提升分解影像穩定性，有效抑制模態混合與模態分裂現象。
Multi-Dimensional UPEMD 的一大優勢是可大幅減少演算法所需的實現次數。MEEMD 通常需超過 100 次實現，Multi-Dimensional UPEMD 僅需 4 至 8 次均勻相位實現即可達到相同甚至更佳的分解品質。理論分析指出，其計算成本由原本與實現數（n_e）成正比，降低為與相位數（nₚ）成正比，大幅提升運算效率。
為驗證方法效能，本文針對經典影像Lena、合成影像（加入均勻雜訊之二維正弦波）、MRI 醫學影像與小女孩影像進行分解實驗與比較。結果顯示，Multi-Dimensional UPEMD 能有效保留邊界與影像紋理，同時抑制雜訊，並在紋理對比表現上優於 MEEMD。此外，其平均運算時間顯著縮短，提升計算效率。

This study proposes an image decomposition method based on Multi-Dimensional Uniform Phase Empirical Mode Decomposition (Multi-Dimensional UPEMD), as an improvement to the conventional Multi-Dimensional Ensemble Empirical Mode Decomposition (MEEMD). The proposed approach replaces the EEMD component in MEEMD with Uniform Phase EMD, where narrowband sine waves with uniformly distributed phases are employed as deterministic perturbations. This substitution stabilizes the decomposition process and effectively mitigates issues such as mode mixing and mode splitting.
A key advantage of Multi-Dimensional UPEMD is its substantial reduction in the number of required realizations. While MEEMD typically demands over 100 realizations to achieve acceptable decomposition quality, Multi-Dimensional UPEMD achieves comparable or even superior results using only 4 to 32 uniform-phase realizations. Theoretical analysis shows that the computational cost is reduced from being proportional to the number of realizations (n_e) to being proportional to the number of phases (n_p), significantly improving computational efficiency.
To evaluate the performance of the proposed method, experiments were conducted on a variety of images, including the standard Lena image, synthetic images (2D sine waves with uniform noise), MRI medical images, and a real-world image of a young girl. Experimental results demonstrate that Multi-Dimensional UPEMD preserves edge structures and fine textures more effectively while suppressing noise, and it outperforms MEEMD in terms of texture contrast. Moreover, it achieves a notable reduction in average computation time, confirming its practical efficiency.

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