MR and PET/SPECT brain image fusion based on the fractional Hermite transform and sparse representation

Fusion of medical images plays a fundamental role for disease diagnosis and interpretation because it allows the combination of structural and functional modalities to provide more relevant and comprehensive data. The fusion is the process of integrating complementary information from multiple source images into a single composite representation, thereby enhancing interpretability for subsequent analysis. In this work, we propose a novel fusion technique based on the fractional Hermite transform (FrHT) and sparse representation (SR). The method is applied to fusion of MRI and PET/SPECT images of the brain. Specifically, the fusion of Magnetic Resonance Imaging (MRI), which offers high-resolution anatomical detail, with Positron Emission Tomography (PET) or Single Photon Emission Computed Tomography (SPECT), which reveal metabolic and functional activity, enables clinicians and researchers to better localize abnormalities and improve diagnostic accuracy. The FrHT extends the classical Hermite transform providing adjustable fractional orders in the analysis and enhancing feature extraction across multiple domains. Sparce representation is a technique which employs a linear combination of a small number of atoms from an overcomplete dictionary to decompose a signal into a sparse vector. In the proposed framework, coefficients obtained from the FrHT decomposition at different orders are further analyzed using the SR model. The fusion process is performed using the resulting sparse vectors, ensuring that both structural and functional features are preserved during the fusion process. The technique was evaluated on public brain MRI and PET/SPECT images, demonstrating its effectiveness in producing fused images that retain anatomical precision while highlighting functional activity. Typical evaluation metrics for image fusion assessment were used to validate the proposed method. The results suggest that the proposed FrHT-SR approach can serve as a valuable tool in medical imaging, supporting improved visualization and clinical decision-making.