International Journal of Applied Mathematics and Machine Learning

Abstract

In order to achieve the multi-focus image fusion task, a sparse representation method based on quaternion for multi-focus image fusion is proposed in this paper. Firstly, the RGB color information of each pixel in the color image is represented by quaternion based on the relevant knowledge of computational mathematics, and the color image pixel is processed as a whole vector to maintain the relevant information between the three color channels. Secondly, the dictionary represented by quaternion and the sparse coefficient represented by quaternion are obtained by using the our proposed sparse representation model. Thirdly, the coefficient fusion is carried out by using the “max-L1” rule. Finally, the fused sparse coefficient and dictionary are used for image reconstruction to obtain the quaternion fused image, which is then converted into RGB color multi-focus fused image. Our method belongs to computational mathematics, and uses the relevant knowledge in the field of computational mathematics to help us carry out the experiment. The experimental results show that the method has achieved good results in visual quality and objective evaluation.