There is an increasing demand in the scientific visualization community for high quality real time interactive volume renderers; but the goal of high quality in volume rendering degrades the performance of the volume renderer. The current advancements in graphics hardware has resulted in the adoptation of the GPU as a solution for the degradation issue in a volume renderer. However there is a caveat, with the use of the GPU as a solution; as the GPUs memory size and long data transfer times between CPU and GPU limit the performance of the GPU based volume renderer. The GPU based volume renderer performance issue can be resolved by rendering a subset of the pixels. By reducing the volume of data the computational costs are reduced. Then using a GPU based conjugate gradient solver we can reconstruct the full image which has the same quality as the original image. This dissertation will show how using GPUs and compressive rendering will optimize the performance of a volume renderer.