Most existing sparse representation-based approaches for attributed scattering center (ASC) extraction adopt traditional iterative optimization algorithms, which suffer from lengthy computation times and limited precision. This paper presents a solution by introducing an interpretable network that can effectively and rapidly extract ASC via deep unfolding. Initially, we create a dictionary containing reliable prior knowledge and apply it to the iterative shrinkage-thresholding algorithm (ISTA). Then, we unfold ISTA into a neural network, employing it to autonomously and precisely optimize the hyperparameters. The interpretability of physics is retained by applying a dictionary with physical meaning. The experiments are conducted on multiple test sets with diverse data distributions and demonstrate the superior performance and generalizability of our method.