Millions of people in the world are afflicted by visual aberrations. Vision correcting displays help accommodate those with visual aberrations by determining a new image to present the user such that they will see it in focus. This work builds upon previous vision correcting display research by developing and implementing theory that bridges the tradeoff between accuracy and speed that past implementations have faced. In particular, we explore how ideas from compressed sensing can be used to solve the vision correction problem by leveraging sparsity and nonlinear reconstruction techniques. We first model the vision correction problem as a compressive deconvolution problem. We then provide a proof-of-concept implementation which validates the efficacy of the theory for a variety of blur strengths. Next, we propose new techniques for modeling the relationship between the eye and the user's display. Finally, we suggest future directions which can take the proof-of-concept developed in this work and turn it into a practical application for people to use.