With the increasing utilization of X-ray Computed Tomography (CT) in medical diagnosis, obtaining higher quality image with lower exposure to radiation is a highly challenging task in image processing. Sparse representation based image fusion is one of the sought after fusion techniques among the current researchers. A novel image fusion algorithm based on focused vector detection is proposed in this thesis. Firstly, the initial fused vector is acquired by combining common and innovative sparse components of multi-dosage ensemble using Joint Sparse PCA fusion method utilizing an overcomplete dictionary trained using high dose images of the same region of interest from different patients. And then, the strongly focused vector is obtained by determining the pixels of low dose and medium dose vectors which have high similarity with the pixels of the initial fused vector using certain quantitative metrics. Final fused image is obtained by denoising and simultaneously integrating the strongly focused vector, initial fused vector and source image vectors in joint sparse domain thereby preserving the edges and other critical information needed for diagnosis. This thesis demonstrates the effectiveness of the proposed algorithms when experimented on different images and the qualitative and quantitative results are compared with some of the widely used image fusion methods.