As remote sensing image applications are often characterized with limited bandwidth and high-quality demands, higher coding performance of remote sensing images are desirable. The embedded block coding with optimal truncation (EBCOT) is the fundamental part of JPEG2000 image compression standard. However, EBCOT only considers correlation within a sub-band and utilizes a context template of eight spatially neighboring coefficients in prediction. The existing optimization methods in literature using the current context template prove little performance improvements. To address this problem, this paper presents a new mutual information (MI)-based context template selection and modeling method. By further considering the correlation across the sub-bands, the potential prediction coefficients, including neighbors, far neighbors, parent and parent neighbors, are comprehensively examined and selected in such a manner that achieves a nice trade-off between the MI-based correlation criterion and the prediction complexity. Based on the selected context template, a high-order prediction model, which jointly considers the weight and the significance state of each coefficient, is proposed. Experimental results show that the proposed algorithm consistently outperforms the benchmark JPEG2000 standard and state-of-the-art algorithms in term of coding efficiency at a competitive computational cost, which makes it desirable in real-time compression applications, especially for remote sensing images.