Abstract: This paper applies the Empirical Wavelet Transform（EWT） on multi-focus image fusion. EWT is an adaptive signal decomposition method. It has a better performance than empirical mode decomposition and traditional wavelet decomposition in some extent. The key ideal of EWT is realizing the signal decomposition by constructing an adaptive filter bank. However, performing EWT decomposition to each of the two multi-focus images independently may generate two different filter banks and result in mismatch between two corresponding sub-bands to be fused, which will affect the quality of the result image. To solve this problem, a Coordinative Empirical Wavelet Transform（C-EWT） is proposed. Under the C-EWT decomposition, each corresponding sub-band of the two multi-focus images is matched. Furthermore, a new image fusion algorithm based on C-EWT is proposed. The fusion procession is as follows.Firstly, two source images are decomposed into a low frequency sub-band and some high frequency sub-bands, respectively. Then, the low-frequency sub-bands are fused with the fusion rule based on the sum-modified-Laplacian, while the corresponding high-frequency sub-bands are fused with the fusion rule based on the local Log-Gabor energy. Finally, the fused sub-images are combined to reconstruct the fused image. Experiments on four sets of images are conducted to compare the proposed algorithm with other six algorithms. The experimental results have shown that the proposed algorithm has advantages in integrating focus areas, preserving edges and details. Meanwhile, the fusion result by the proposed algorithm has more satisfying visual effect and its objective evaluation index is the closest to the standard fusion image.

Key words: multi-focus image fusion, empirical wavelet transform, coordinate, sum-modified-Laplacian, Log-Gabor energy

摘要： 提出了可协调经验小波变换，并将其应用于多聚焦图像融合。经验小波变换（EWT）是一种自适应信号分解方法，具有比经验模态分解和传统小波分解更好的特性。其核心思想是通过构造自适应的滤波器实现对信号的自适应分解。但是若直接对两幅多聚焦图像分别进行EWT分解，因各自生成的经验小波互不相关，将出现分解所得对应子带不匹配的情况，影响融合图像的质量。针对这一问题，提出了一种可协调的经验小波变换（C-EWT），C-EWT分解下的两个多聚焦图像的对应子带是完全匹配的。基于此，利用C-EWT提出了一种新的多聚焦图像融合算法。每幅源图像经过C-EWT分解后，得到一个低频分量和多个高频分量; 对低频分量采用基于改进Laplacian能量和的阈值匹配选择与加权规则进行融合，对高频分量则采用局部Log-Gabor能量取大的融合规则；将融合之后的各子带分量进行重构得到融合图像。仿真实验表明：与其他六种融合算法相比，所提算法在融合聚焦区域、保留边缘和细节信息方面具有优势，融合图像具有更好的视觉效果，且客观评价指标与标准图像最为接近。

关键词: 多聚焦图像融合, 经验小波变换, 可协调, 改进Laplacian能量和, Log-Gabor能量