Sparse-Based Medical Image Fusion Using a Novel Optimal Dictionary Strategy and Shearlet Transform

Combination of multi-scale transformations and sparse representation (SR) is one of the most useful techniques for fusion of multi modal images. Discrete Shearlet Transform (DST) is one of the directional transforms that is proper to merge MRI and PET scan images. Here, grey-level hit or miss transform (HMT) and matched filter are used to convert both modalities to image patches and form the dictionary of sparse coding. Finally, PCA is utilized to get more important atoms, because the number of atoms is one of important issues. The fusion rule for high frequency components is averaging and weighted averaging is considered for low frequency components. This fusion rule properly demonstrates fused image and induces to visual enhancement. The proposed dictionary has salient results in terms of: mutual information (MI), visual information fidelity (VIF) and correlation coefficients (SCC and PCC); compared to other dictionary learning strategies which are K-SVD and recursive least square (RLS) methods.