Multi-Modal Medical Image Fusion With Geometric Algebra Based Sparse Representation

Multi-modal medical image fusion can reduce information redundancy, increase the understandability of images and provide medical staff with more detailed pathological information. However, most of traditional methods usually treat the channels of multi-modal medical images as three independent grayscale images which ignore the correlation between the color channels and lead to color distortion, attenuation and other bad effects in the reconstructed image. In this paper, we propose a multi-modal medical image fusion algorithm with geometric algebra based sparse representation (GA-SR). Firstly, the multi-modal medical image is represented as a multi-vector, and the GA-SR model is introduced for multi-modal medical image fusion to avoid losing the correlation of channels. Secondly, the orthogonal matching pursuit algorithm based on geometric algebra (GAOMP) is introduced to obtain the sparse coefficient matrix. The K-means clustering singular value decomposition algorithm based on geometric algebra (K-GASVD) is introduced to obtain the geometric algebra dictionary, and update the sparse coefficient matrix and dictionary. Finally, we obtain the fused image by linear combination of the geometric algebra dictionary and the coefficient matrix. The experimental results demonstrate that the proposed algorithm outperforms existing methods in subjective and objective quality evaluation, and shows its effectiveness for multi-modal medical image fusion.