The Bayesian compressive sensing (BCS) is an available approach for data compressions based on compressed sensing framework. Moreover, the priors of sparse signals play a key role in BCS. Various studies that exploit the priors only via models generating, which exist the low prior utilizations. Therefore, to fully use the priors for signals recovering, we propose a novel deep heterogeneous optimization framework which can completely express the priors in a data-model double driven manner. Our work can be briefly summarized by the following aspects. As the heterogeneous handles benefiting recovery solutions, we firstly exploit the available heterogeneous arrangements for traditional BCS recovery models. Secondly, inspired by the deep neural networks (DNNs), we do researches on adding a deep optimization scheme for the scale parameters of heterogeneous prior functions via supervised learning. In addition to developing the three complete algorithms with that merge the prior parameters learning and signal recoveries. Finally, Experimental results show that for both synthetic data and images data our proposed double driven framework achieves the superior performances compared with that of the other well-known compressed recovery algorithms no matter in noise-free or noisy measurement environments.