While traditional imaging systems directly measure scene properties, computational imaging systems add computation to the measurement process, allowing such systems to extract non-trivially encoded scene features. This dissertation demonstrates that exploiting structure in this process allows to even recover information that is usually considered to be completely lost. Relying on temporally and spatially convolutional structure, we extract two novel image modalities that were essentially “invisible” before: a new temporal dimension of light propagation, and a new per-pixel radial velocity dimension, both obtained using consumer Time-of-Flight cameras. These two novel types of images represent first steps toward the inversion of light trans...