<p>This study presents an innovative matrix completion method for estimating the direction of arrival (DOA) using acoustic vector sensor array (AVSA) with missing data. The signal restoration task is initially framed as a matrix factorization problem, where the nuclear norm minimization is equivalently transformed into a multiple Frobenius norms minimization problem through matrix bilinear factorization decomposition. On this basis, to address noise sensitivity and preserve signal structures, a graph Laplacian regularization (GLR) term is incorporated into the multiple Frobenius norms minimization problem to preserve local structures and features to mitigate the effect of the noise. Furthermore, the UV decomposition matrix completion model based on graph Laplacian regularization (UVGLR-MC) is proposed. Then, the information acquired from the array to be retrieved is processed using the alternating direction multiplier method (ADMM) methodology. The multiple signal classification (MUSIC) method is employed to determine the DOA of the signal. Simulation outcomes show that this strategy exhibits excellent robustness and computational efficiency when handling complex datasets with noise and missing data.</p>