Functional and Anatomical Image Fusion Based on Gradient Enhanced Decomposition Model

Medical image fusion technology can synthesize complementary information from multimodal medical images while saving storage costs. Targeting the problems of reduced contrast, blurred details, color distortion, and excessive processing time requirement in fusion algorithms, we propose a new functional and anatomical image fusion algorithm based on a gradient enhanced decomposition model. First, a new gradient-enhanced decomposition (GED) model is proposed. Subsequently, the proposed GED model is expanded into a three-layer decomposition, wherein the input image is decomposed into a basic, local mean energy, and texture layers using the alternating direction method of multipliers. Compared with other classic decomposition methods, the proposed three-layer decomposition has the advantages of no additional noise and requiring less time while enhancing gradient. Second, we propose targeted fusion rules for each layer. After the basic layer is weighted and averaged, the gamma function is used to adjust its brightness. The product of the local
$l_{2}$
norm and the largest singular value constitutes the fusion weights of the local mean energy layers. The fusion weights of the texture layers are determined by the product of the local
$l_{1}$
norm and the largest singular value. Finally, the fused image is reconstructed. We perform numerous experiments to prove that the proposed fusion algorithm provides clearer edge details and superior colors in a short processing time, and there was a statistically significant difference compared with other classical algorithms.