Based on the persistence and exponential decay across scales of Tetrolet coefficients, the Tetrolet-domain universal hidden Markov tree structured sparse prior model was established for compressive imaging. In this model, the statistic distribution of Tetrolet coefficients was presented as the prior with the Gaussian-mixture form, and then, the posterior probability density function (PDF) was estimated by using the factor graph method. In order to solve the problem that the messages passing through the loop factor graph cannot reach stable convergence, the Turbo equalization method was exploited to decouple the factor graph into two parts for estimating the states of compressive sampling and the structured sparse model. Then, the exchange of messages was performed mutually in the two sub-graphs until reaching convergence. Finally, the image was estimated based on the minimum mean-squared error criterion. The normalized mean-squared error of reconstructing the testing image with size 128×128 was -20.97 dB, and the run-time was 45.24 s. Experimental results demonstrate that the proposed algorithm outperforms the algorithms based on the wavelet-domain hidden Markov tree model in terms of reconstruction quality and speed.