To resolve the problems of scattered focus-edge blurring, artifacts, and block effects during the multifocus image fusion, an algorithm based on low-rank and sparse matrix decomposition (LRSMD) and discrete cosine transform (DCT) is designed to achieve the multifocus image fusion. First, the source images were decomposed into low-rank and sparse matrices using LRSMD. Subsequently, the DCT-based method was designed for detecting the focus regions in the low-rank matrix part and obtaining the initial focus decision map. The decision map was verified using the repeated consistency verification method. Meanwhile, the fusion strategy based on morphological filtering was designed to obtain fusion results of the sparse matrix. Finally, the two parts were fused using the weighted reconstruction method. The experimental results show that the proposed algorithm has the advantages of high clarity and full focus in subjective evaluations. The best results for the four metrics, including edge information retention, peak signal-to-noise ratio, structural similarity, and correlation coefficient in objective evaluations, improved by 62.3%, 6.3%, 2.2%, and 6.3%, respectively, compared with the other five mainstream algorithms. These improvement results prove that the proposed algorithm effectively improves focused information extraction from source images and enhances the focused edge detail information. Furthermore, the algorithm is crucial for reducing the artifact and block effects.