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A traditional camera requires the photographer to select the focus,ISO, exposure and aperture at capture time. While advances in light field photography has enabled for post-capture control of focus and perspective, they suffer from several limitations including lower spatial resolution, need for hardware modifications,and restrictive choice of f-numbers and focal lengths. In this paper, we propose Compressive Epsilon Photography a technique for achieving complete post-capture control of focus and aperture in a traditional camera by acquiring a carefully selected set of images(about 16) and computationally reconstructing images corresponding to all other focus-aperture settings. Our approach has the following distinct contributions: first, we learn the statistical redundancies in a complete focal-aperture stack data using a Gaussian Mixture Model; second, we derive a greedy sampling strategy for selecting the best focus-aperture settings and third, we develop an algorithm for reconstructing the entire focal-aperture stack data from a few captured images. As a consequence, at capture time, only a burst of images with carefully selected focal-aperture settings are acquired. Post-capture, the user can then select any focalaperture setting of choice and the corresponding image can be rendered using our algorithm. We show extensive results on several real data sets captured using an SLR camera.