With the recent availability of commercial light field cameras, we can foresee a future in which light field signals will be as common place as images. Hence, there is an imminent need to address the problem of light field processing. We provide a common framework for addressing many of the light field processing tasks, such as denoising, angular and spatial superresolution, etc. (in essence, all processing tasks whose observation models are linear). We propose a patch based approach, where we model the light field patches using a Gaussian mixture model (GMM). We use the ”disparity pattern” of the light field data to design the patch prior. We show that the light field patches with the same disparity value (i.e., at the same depth from the focal plane) lie on a low-dimensional subspace and that the dimensionality of such subspaces varies quadratically with the disparity value. We then model the patches as Gaussian random variables conditioned on its disparity value, thus, effectively leading to a GMM model. During inference, we first find the disparity value of a patch by a fast subspace projection technique and then reconstruct it using the LMMSE algorithm. With this prior and inference algorithm, we show that we can perform many different processing tasks under a common framework.