1. A method for reconstructing a layered form of a three-dimensional scene from a light field of the scene, the method comprising a computer system executing the steps of: assuming one or more masks, then estimating, based on the scene light field and on the assumed one or more masks, atom coefficients for layer light fields for two or more layers representing different depths of the scene, wherein the layer light fields are represented as linear combinations of atoms selected from an overcomplete dictionary and the linear combinations are weighted by the atom coefficients, and wherein the masks represent the occlusion of backward layers by forward layers; assuming the layer light fields, then estimating the masks based on the assumed layer light fields; iteratively performing the steps of estimating atom coefficients for layer light fields and estimating the masks; and estimating layers of a three-dimensional scene from the layer light fields and the masks.