Acoustic imaging is a standard technique for mapping positions and powers of acoustic sources using microphone arrays, which often causes an ill-posed inverse problem. In this article, we firstly improve the forward model of acoustic power propagation by considering background noises at the sensor array, and the propagation uncertainty caused by wind tunnel effect. We then propose a robust super-resolution approach via sparsity constraint for the acoustic imaging in strong background noises. The sparsity parameter is adaptively derived from the sparse distribution of source powers. The proposed approach can jointly reconstruct source powers and positions, as well as the background noise power. Our approach is compared with the conventional beamforming, deconvolution and sparse regularization methods by simulated, real data and hybrid data respectively. It is feasible to apply our approach for mapping complex monopole sources using the 2D non-uniform microphone array in wind tunnel tests.