In exemplary implementations of this invention, a light field camera uses a light field dictionary to reconstruct a 4D light field from a single photograph. The light field includes both angular and spatial information and has a spatial resolution equal to the spatial resolution of the imaging sensor. Light from a scene passes through a coded spatial light modulator (SLM) before reaching an imaging sensor. Computer processors reconstruct a light field. This reconstruction includes computing a sparse or compressible coefficient vector using a light field dictionary matrix. Each column vector of the dictionary matrix is a light field atom. These light field atoms each, respectively, comprise information about a small 4D region of a light field. Reconstruction quality may be improved by using an SLM that is as orthogonal as possible to the dictionary.