Existing image fusion algorithms have some problems caused by non-linear operations, such as noise interference and spatial complexity, which make fused images easy to cause distortion and information loss. Compressed sensing image fusion algorithms proposed by some scholars can effectively improve this problem. However, most of them neglect the low rank of image matrix, thus often reducing the quality of fusion. Thus, combining the compressed sensing fusion technology with the low rank matrix approximation method, we propose an image fusion method based on information theory image difference and adaptive weighted kernel norm minimization. The method consists of three stages. Firstly, the two source images are sparsed by wavelet sparse basis, and the measurement output matrix is obtained by compressing the samplings with structural random matrix. Then, the measurement output matrix is divided into blocks, and the fused measurement output matrix blocks are obtained by using the image difference fusion algorithm. Finally, the block weights obtained by adaptive weighted kernel norm minimization method are used to reconstruct the fused image by the orthogonal matching pursuit method. Experimental results verify the validity and universality and show that our method is superior to other fusion algorithms in many evaluation indexes.