With the increasing utilization of X-ray Computed Tomography (CT) in medical diagnosis, obtaining higher quality image with lower exposure to radiation has become a highly challenging task in image processing. In this paper, a novel sparse fusion algorithm is proposed to address the problem of lower Signal to Noise Ratio (SNR) in low dose CT images. Initial fused image is obtained by combining low dose and medium dose images in sparse domain, utilizing the Dual Tree Complex Wavelet Transform (DTCWT) dictionary which is trained by high dose image. And then, the strongly focused image is obtained by determining the pixels of source images which have high similarity with the pixels of the initial fused image. Final denoised image is obtained by fusing strongly focused image and decomposed sparse vectors of source images, thereby preserving the edges and other critical information needed for diagnosis. This paper demonstrates the effectiveness of the proposed algorithm both quantitatively and qualitatively.