Abstract: Aiming at the imaging characteristics of multi-focus image and multi-modality medical image, and considering with the properties of shearlet transform which can capture more directions and other geometric information of images, an image fusion method based on non-subsample shearlet transform using compressed sensing combined with regional characteristics is proposed. Multi-scale and multi-directional decompositions of source images are performed by non-subsampled shearlet trasnform. The decomposition of low frequency sub-band coefficients are merged by the regional energy and regional variance adaptive weighted fusion rule. Since the decomposed high frequency sub-band coefficients have high sparsity, it can be compressed by the Gaussian random measurement matrix, the fusion rule of the absolute value based on compressed sensing is adopted to fusion. Afterwards, it uses the orthogonal matching pursuit algorithm for reconstruction. And the fusion image is obtained by non-subsampled shearlet trasnform inverse transformation. The simulation results show that the image fusion effect of this method has better advantages in both subjective and objective evaluation than other traditional fusion methods.

Key words: non-subsample shearlet transform, regional characteristics, Gaussian random measurement matrix, orthogonal matching pursuit algorithm

摘要： 针对多聚焦图像和多模态医学图像的成像特性，结合剪切波变换可以捕捉图像更多的方向和其他几何信息的特点，提出一种利用非下采样剪切波变换的压缩感知与区域特性相结合的图像融合方法。利用非下采样剪切波变换将源图像进行多方向、多尺度的分解，将得到的低频子带系数采取区域能量与区域方差加权的自适应融合方式处理。由于分解后的高频子带系数具有高稀疏性，可将高频子带系数通过高斯随机测量矩阵进行压缩处理之后，采用基于压缩感知的绝对值取大的融合方式处理；然后利用正交匹配追踪算法重构，经过非下采样剪切波变换逆变换得到融合图像。仿真实验结果表明，该方法的图像融合效果无论是在主观感觉还是客观指标评价方面较传统的融合方法都具有较大优势。

关键词: 非下采样剪切波变换, 区域特性, 高斯随机测量矩阵, 正交匹配追踪算法