Image reconstruction from limited and/or sparse data is known to be an ill-posed problem and a priori information/constraints have played an important role in solving the problem. Early constrained image reconstruction methods utilize image priors based on general image properties such as sparsity, low-rank structures, spatial support bound, etc. Recent deep learning-based reconstruction methods promise to produce even higher quality reconstructions by utilizing more specific image priors learned from training data. However, learning high-dimensional image priors requires huge amounts of training data that are currently not available in medical imaging applications. As a result, deep learning-based reconstructions often suffer from two known practical issues: a) sensitivity to data perturbations (e.g., changes in data sampling scheme), and b) limited generalization capability (e.g., biased reconstruction of lesions). This paper proposes a new method to address these issues. The proposed method synergistically integrates model-based and data-driven learning in three key components. The first component uses the linear vector space framework to capture global dependence of image features; the second exploits a deep network to learn the mapping from a linear vector space to a nonlinear manifold; the third is an unrolling-based deep network that captures local residual features with the aid of a sparsity model. The proposed method has been evaluated with magnetic resonance imaging data, demonstrating improved reconstruction in the presence of data perturbation and/or novel image features. The method may enhance the practical utility of deep learning-based image reconstruction.