We present a compressed sensing framework for reconstructing the full light field of a scene captured using a single-sensor consumer camera. To achieve this, we use a color coded mask in front of the camera sensor. To further enhance the reconstruction quality, we propose to utilize multiple shots by moving the mask or the sensor randomly. The compressed sensing framework relies on a training based dictionary over a light field data set. Numerical simulations show significant improvements in reconstruction quality over a similar coded aperture system for light field capture.