In many applications, it is critical to be able to sample the most informative pixels of an image first; and then once these pixels are sampled, the highest fidelity image can be reconstructed. Optimized sampling strategies generally fall into two categories: static and dynamic. In dynamic sampling, each new sample is chosen by using information obtained from previous samples. In this way, dynamic sampling offers the potential of much greater fidelity, but at the cost of greater complexity. Existing methods for dynamic non-uniform sampling of images are based on the intuition that sampling rates should be greatest in locations of greatest variation, but recent developments in the theory of optimal experimental design offer a theoretical framework for optimal sampling based on the use of a formal Bayesian prior model. In this paper, we introduce a fast dynamic image sampling framework based on Bayesian experimental design (BED). The method, which we call model-based dynamic sampling (MBDS) allows for the use of a general prior distribution for the image, and it incorporates a pixel-wise sampling constraint in the BED framework. The MBDS works by first generating L stochastic samples (i.e., images) from the posterior distribution given the current measurements, and then selecting the pixel with the greatest posterior variance. We also introduce a computationally efficient method for computing the stochastic samples through a local updating technique.