Robust multi-modal medical image fusion via anisotropic heat diffusion guided low-rank structural analysis

This paper proposes a novel and robust multi-modal medical image fusion method, which is built upon a novel framework comprising multi-scale image decomposition based on anisotropic heat kernel design, scale-aware salient information extraction based on low-rank analysis, and scale-specific fusion rules. Our framework respects multi-scale structure features, while being robust to complex noise perturbation. First, anisotropic heat kernel is computed by constructing an image pyramid and embedding multi-level image properties into 2D manifolds in a divide-and-conquer way, consequently, multi-scale structure-preserving image decomposition can be accommodated. Second, to extract meaningfully scale-aware salient information, we conduct low-rank analysis over the image layer groups obtained in the first step, and employ the low-rank components to form the scale space of the salient features, wherein the underlying noise can be synchronously decoupled in a natural way. Third, to better fuse the complementary salient information extracted from multi-modal images, we design an S-shaped weighting function to fuse the large-scale layers, and employ the maximum selection principle to handle the small-scale layers. Moreover, we have conducted extensive experiments on MRI and PET/SPECT images. The comprehensive and quantitative comparisons with state-of-the-art methods demonstrate the informativeness, accuracy, robustness, and versatility of our novel approach.