Compressive rendering refers to the process of reconstructing a full image from a small subset of the rendered pixels, thereby expediting the rendering task. Images produced via direct volume rendering are usually highly compressible in a transform domain such as the Fourier or wavelet domains. In this dissertation, we empirically investigate four image order tech- niques for compressive rendering that are suitable for direct volume rendering. The first technique is based on the theory of compressed sensing and leverages the sparsity of the image gradient in the Fourier domain. Following this, we investigate sparse representation of volume rendered images via dictionary learning. The latter techniques exploit smoothness properties of the rendered image; the third technique recovers the missing pixels via a to- tal variation minimization procedure while the fourth technique incorporates a smoothness prior in a variational reconstruction framework employing interpolating cubic B-splines. We compare and contrast these four techniques in terms of quality, efficiency and sensitivity to the distribution of pixels. Our results show that smoothness-based techniques significantly outperform techniques that are based on compressed sensing as well as dictionary learning and are also robust in the presence of highly incomplete information. We achieve high quality recovery with as little as 20% of the pixels distributed uniformly in screen space.