An Innovative Low-Rank Sparse Matrix Decomposition Clutter Suppression Method Based on Non-Convex Alternatives for Pseudo-Random-Coded Ground-Penetrating Radar

This article analyzes the composition and characteristics of echo signals in a pseudorandom-coded ground-penetrating radar (GPR). Based on these characteristics, an innovative low-rank sparse matrix decomposition (LRSD) method is developed using equivalent matrix gamma norm (EMGN) and equivalent minimax-concave penalty (EMCP) to suppress clutter in the echo signals. The proposed method employs non-convex alternatives to the matrix rank and sparsity functions. Therefore, it can alleviate biased estimates of the matrix rank and sparsity of the pseudorandom-coded radar’s received signals. The proposed method is verified by simulations and experiments on a real dataset. The results demonstrate that the proposed method can achieve better performance in terms of signal-to-clutter ratio (SCR) than the robust nonnegative matrix factorization (RNMF) and robust principal component analysis (RPCA) methods.