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Target detection in side-scan sonar images plays a significant role in ocean engineering. However, the target images are usually severely interfered by the complex background and strong environmental noise, which makes it difficult to extract robust features from small targets and makes the target detection task quite challenging. In this paper, a novel small target detection method in sonar images is proposed based on the low-rank sparse matrix factorization. Initially, the side-scan sonar images are preprocessed so as to highlight the individual differences of the target. Then, the problems of target feature extraction and noise removal are characterized as the problem of matrix decomposition. An improved Robust Principal Component Analysis algorithm is used to extract target information, and the fast proximal gradient method is used to optimize the solution. The original sonar image is reconstructed into the low-rank background matrix, the sparse target matrix, and the noise matrix. Eventually, a morphological operation is used to filter out the noise and refine the target edges in the target matrix for improving the accuracy of target detection. Experimental results show that the proposed method not only achieves better detection performance in comparison to the conventional baseline algorithms but also performs robustly in various signal-to-clutter ratio conditions.