Abstract: In rendering applications, we are often faced with the problem of computing the integral of an unknown function. Typical approaches used to estimate these integrals are often based on Monte Carlo methods that slowly converge to the correct answer after many point samples have been taken. In this work, we study this problem under the framework of compressed sensing and reach the conclusion that if the signal is sparse in a transform domain, we can evaluate the integral accurately using a small set of point samples without requiring the lengthy iterations of Monte Carlo approaches. We demonstrate the usefulness of our framework by proposing novel algorithms to address two problems in computer graphics: image antialiasing and motion blur. We show that we can use our framework to generate good results with fewer samples than is possible with traditional approaches.