针对甲状腺肿瘤超声图像对比度低和SPECT 图像边界模糊的特点，结合多尺度几何分析和单尺度稀疏表示的思想，提出了一种Shearlet 变换与稀疏表示相结合的图像融合算法。首先，用该变换对已经精确配准的源图像进行分解，得到图像的高低频子带系数。对稀疏性较差的低频子带系数进行字典训练并求解其稀疏表示系数，并采用能量值取大的规则进行融合。高频子带系数采用区域拉普拉斯能量和的规则。最后，用Shearlet 逆变换得到融合图像。实验结果表明，此算法在主观视觉效果和客观评价指标上优于多尺度融合方法和单尺度下基于稀疏表示的图像融合方法。

According to the characteristics of ultrasound images with low contrast and SPECT images with blurred boundary, combining the theory of multi-scale geometric analysis with single scale sparse representation, an image fusion algorithm based on Shearlet transform and sparse representation is proposed. Firstly, the Shearlet transform is used to decompose the registered source images, thus the low frequency sub-band coefficients and high frequency sub-band coefficients can be obtained. The low frequency sub-band coefficients with lower sparseness are used to train the dictionary and the sparse representation coefficients are calculated by the trained dictionary, and the fusion rule of the sparse representation coefficients is used to select the larger energy. The high frequency sub-band coefficients are fused by the region sum modified laplacian. Finally, the fused image is reconstructed by inverse Shearlet transform. The experimental results demonstrate that the proposed method outperforms the multi-scale methods and the methods of sparse representation in single scale in term of visual quality and objective evaluation.