Coded masks are frequently used imaging techniques for imaging in X- and gammaray astronomy. Instead of traditional optics, coded mask telescopes use a heavy metal plate with a pattern of apertures which modulate the incoming radiation, which is then recorded by a position sensitive detector. A map of the sky is then obtained by decoding the detector image, normally by means of cross-correlation. The technique is designed to operate with static pointings, during which an image of the mask is accumulated on the detector. In this thesis an alternative method of reconstruction is proposed where each detected photon is projected back to all the regions of the sky that it may have originated from. This photon-by-photon approach allows the production of images even when the telescope is moving. This thesis presents the sky maps obtained applying the back-projection method to a prototype data set collected by INTEGRAL/ISGRI during slews in a 10 orbit period in October 2010. Analysing the entire INTEGRAL slew data set would permit the use of approximately 65Ms of data so far unexplored observations. Production of all-sky maps, source lists and flux-calibrated light- curves have all been demonstrated. The second part of this thesis applies the same back-projection method to near-field medical gamma-ray imaging. Medical imaging could benefit from the high sensitivity that coded aperture images have demonstrated in astronomy, overcoming limitations imposed by collimators. Furthermore, the intrinsic depth perception of coded mask cameras makes it possible to obtain 3D images of a source distribution with just one or two views. A 3D near-field coded mask camera was designed, assembled and tested. The back-projection algorithm was applied to data obtained with isotopes typically used in nuclear medical imaging. Coded-mask medical imaging systems have the potential to reduce the scan time or patient dose and the footprint of the scanning systems. The successful reconstruction of multiple point sources and extended sources with a large field of view using two simultaneous camera views was demonstrated.