Difference images quantify changes in the object scene over time. In this paper, we use the feature-specific imaging paradigm to present methods for estimating a sequence of difference images from a sequence of compressive measurements of the object scene. Our goal is twofold. First is to design, where possible, the optimal sensing matrix for taking compressive measurements. In scenarios where such sensing matrices are not tractable, we consider plausible candidate sensing matrices that either use the available a priori information or are nonadaptive. Second, we develop closed-form and iterative techniques for estimating the difference images. We specifically look at l2 - and l1 -based methods. We show that l2-based techniques can directly estimate the difference image from the measurements without first reconstructing the object scene. This direct estimation exploits the spatial and temporal correlations between the object scene at two consecutive time instants. We further develop a method to estimate a generalized difference image from multiple measurements and use it to estimate the sequence of difference images. For l1-based estimation, we consider modified forms of the total-variation method and basis pursuit denoising. We also look at a third method that directly exploits the sparsity of the difference image. We present results to show the efficacy of these techniques and discuss the advantages of each.