Image watermarking technology poses a significant challenge, requiring a delicate balance between robustness, imperceptibility, and capacity. To solve the balancing problem, a statistical learning based blind image watermarking technique is proposed in this paper. The idea of the proposed method to solve the balancing problem is to enhance imperceptibility and robustness while accommodating sufficient watermarks. Firstly, the local low-order pseudo-Zernike moments (PZM) magnitude in the discrete non-separable Shearlet transform (DNST) domain is constructed as the embedding domain. To ensure stability in embedding positions, we propose an edge embedding strategy. Secondly, by analyzing the statistical characteristics and multi-correlations of DNST-PZM magnitudes, a multi-correlation vector model based on the skew student's-t mixture (SSM) and hidden Markov tree (HMT) is designed. Finally, leveraging the vector SSM-HMT model and the maximum likelihood (ML) criterion, we derive the closed-form decoder expression. Comparative analysis with state-of-the-art methods demonstrates the superior imperceptibility and robustness of our proposed approach in accommodating the same capacity watermark.