Representative Coefficient Total Variation for Efficient Infrared Small Target Detection

Low-rank and sparse decomposition (LRSD)-based models are powerful and robust tools for infrared small target detection. However, due to the calculation of singular value decomposition (SVD) and the optimization of complex regularization terms, the existing low-rank models often suffer from high computational complexity. To solve this problem, based on the theorem that representative coefficient matrix obtained by orthogonal transformation of data matrix can inherit the spatial structure of data matrix, we propose a representative coefficient total variation (RCTV) method for efficient infrared small target detection. In our method, we use total variational to constraint representative coefficient matrix instead of data matrix to describe local smooth prior, which helps remove noise and reduce computational complexity. Meanwhile, we control the number of columns in the representative coefficient matrix to maintain the low-rank characteristics of background, which avoids SVD calculation and improves the detection efficiency. Therefore, RCTV regularization can simultaneously describe local smooth prior and low-rank prior. Moreover, to better enhance the sparsity of targets and distinguish sparse nontarget points, we use the log-sum function to adaptively assign weights to targets. It helps obtain more accurate detection performance. The proposed model is efficiently solved by the alternating direction multiplier method (ADMM). A large number of experiments show that the proposed method is superior to the existing low-rank methods in both detection accuracy and efficiency.