The array manifold matrix was constructed as a redundant dictionary in which the array receiving signals were sparse through the appropriate spatial sparse division, and the corresponding L₁-analysis sparse recovery model was established to reconstruct the array output data. The core of this paper is to prove that the manifold matrix is a tight frame and can satisfy the condition which guarantees the accurate recovery of signals through L₁-analysis sparse recovery so that it is reasonable enough to use L₁-analysis sparseness optimization to reconstruct the array output data. The upper bound of reconstruction error was given. The effectiveness of this presented method for improving the performance of DOA estimation with low SNR was verified by the experiments using the actual measurement data received in microwave darkroom through MUSIC algorithm.