Most of the existing Beamforming methods are based on the assumptions that the sources are all point sources and the angular separation between the direction of arrival (DOA) of the source and the interference is large enough to assure good performance. In this paper, we consider a tough scenario where the target source and the interference are simultaneously spatially distributed and overlapped. To improve the performance of Beamforming in this scenario, we propose two approaches: the first approach exploits the non-Gaussianity as well as the spectrogram sparsity of the output of the microphone array; the second approach exploits the generalized sparsity with overlapped groups of the Beampattern. The proposed criteria are solved by methods based on linearized preconditioned alternating direction method of multipliers (LPADMM) with high accuracy and high computational efficiency. Numerical simulations and real data experiments show the advantages of the proposed approaches compared to previously proposed Beamforming methods for signal enhancement.