This paper examines the performance of Hidden Markov Tree model based weights in reconstruction quality for an existing task-aware compressive video coding system which aims object detection specifically. The existing system utilizes weights in reconstruction which are computed by tracking of the foreground object. The proposed system acquires similar average PSNR with the existing one which reported some improvement compared to the conventional unweighted reconstruction at low sampling rates. Furthermore, it is a little bit better than the existing system at higher sampling rates. It can be inferred from this study that Bayesian approaches that take account structural dependencies between transformation coefficients has the potential of improving reconstruction quality for such a compressive video coding system with object detection task.