Medical image fusion is designed to help physicians in their decisions by providing them with a preclinical image with enough information. Accurate assessment and effective treatment of the disease reduce the time it takes to relieve the symptoms of the disease. This article utilizes an effective data fusion approach to work on two different imaging modalities; computed tomography (CT) and magnetic resonance imaging (MRI). The data fusion approach is based on the combination of singular value decomposition (SVD) and the Fast Discrete Curvelet Transform (FDCT) techniques to reduce processing time during the fusion process. The SVD-FDCT data fusion approach is being tested with two multimodal medical image fusion applications. The first application concerns the detection of liver lesions and the second application concerns the early detection of acute intracerebral hemorrhage. Experimental tests demonstrate that not only the SVD-FDCT data fusion algorithm can treat the curved objects and edges effectively as the FDCT do. But also, the throughput of the fusion algorithm is comparable to related fusion algorithms such as principal component analysis (PCA), Transform and Discrete Wavelet Transform (DWT), dual-tree complex wavelet transform (DT-CWT), and Curvelet fusion algorithms.