Acoustic imaging is a powerful tool to localize and reconstruct source powers using microphone array. However, it often involves the ill-posed inversions and becomes too time-consuming to obtain high spatial resolutions. In this paper, we firstly propose a shift-invariant convolution model to approximate the forward model of acoustic power propagation. The convolution kernel is derived from the Symmetric Toepliz Block Toepliz (STBT) structure of propagation matrix. Then we propose a hierarchical Bayesian inference approach via Variational Bayesian Approximation (VBA) criterion in order to achieve robust acoustic imaging in colored background noises. For super spatial resolution and wide dynamic power range, we explore the Student's-t prior on the acoustic power distribution thanks to the sparsity and heavy tail of prior model. Colored noise distributions are also modeled by the Student's-t prior, and this does not excessively penalize large model errors as the Gaussian white prior does. Finally proposed 2D convolution model and VBA approach are validated through simulations and real data from wind tunnel compared to classical methods.