Single Photon Avalanche Photodiodes (SPADs) have recently received a lot of attention in imaging and vision applications due to their excellent performance in low-light conditions, as well as their ultra-high temporal resolution. Unfortunately, like many evolving sensor technologies, image sensors built around SPAD technology currently suffer from a low pixel count. In this work, we investigate a simple, low-cost, and compact optical coding camera design that supports high resolution image reconstructions from raw measurements with low pixel counts. We demonstrate this approach for regular intensity imaging, depth imaging, as well transient imaging. Our method uses an end-to-end framework to simultaneously optimize the optical design and a reconstruction network for obtaining super-resolved images from raw measurements. The optical design space is that of an engineered point spread function (implemented with diffractive optics), which can be considered an optimized anti-aliasing filter to preserve as much high resolution information as possible despite imaging with a low pixel count, low fill-factor SPAD array. We further investigate a deep network for reconstruction. The effectiveness of this joint design and reconstruction approach is demonstrated for a range of different applications, including high speed imaging, and time of flight depth imaging, as well as transient imaging. While our work specifically focuses on low-resolution SPAD sensors, similar approaches should prove effective for other emerging image sensor technologies with low pixel counts and low fill-factors.