In this paper, we propose a structured iterative alternating sparse matrix decomposition to efficiently decompose the input multidimensional data from active thermography into the sum of a low-rank matrix, a sparse matrix, and a noise matrix. In particular, the sparse matrix is further factorized into a pattern constructed dictionary matrix and a coefficient matrix. The estimation of the dictionary matrix and coefficient matrix is based on integrating the vertex component analysis with the framework of the alternating direction method of multipliers. In addition, the joint structure sparsity and nonnegative constraint are emphasized as part of the learning strategy. In order to verify the effectiveness and robustness of the proposed method, experimental studies have been carried out by applying the proposed method to thermal imaging diagnostic system for carbon fiber reinforced plastics (CFRP) defects detections. The validation study has been conducted by comparing the proposed method with the current state-of-the-art algorithms. The results indicate that the proposed method significantly improves the contrast ratio between the defective regions and the non-defective regions.