Application of the CLEAN algorithm to three dimensional coded aperture imaging

Abstract

An iterative technique for the removal of artifacts caused by the near field effects of a coded aperture imaging system is presented. The technique, which we call z-Clean, first locates high energy sources within a three dimensional field of view using a least squares method and then removes the artifacts using a method similar to that of the CLEAN algorithm used in radio astronomy, but instead operating in the detector shadowgram domain rather than the final image domain. Computer simulations were performed of observations of four point sources of different intensities and at different depths from the detector. Both a continuous detector of 1 cm FWHM detection capability and a pixellated detector with 0.2 cm square pixels were investigated using a Modified Uniformly Redundant Array coded aperture of element size 0.6 cm. The efficacy of the z-Clean technique for artifact removal is demonstrated for both detector types for the three strongest sources of 100kBq, 50kBq and 10kBq using plane separations of 2 cm, 1 cm, 0.5 cm and 0.1 cm, to leave only small ghosts lying up to around 2 cm from the reconstructed source depth. For twenty trials of each observation, the three strongest sources are reconstructed no further than 0.7 cm from the closest plane with many being from 0 cm to 0.5 cm for both detector types. The depth location for all three strongest sources using both detector types is no worse than 0.5 cm from the actual source depth and is in most cases much better, being closer than 0.1 cm for the strongest source at plane separations of 1 cm, 0.5 cm and 0.1 cm. z-Clean was not able to remove the artifacts nor determine accurately the depth of the weakest source of 5kBq and in general sources that experience a phasing error are less accurately located although still better than 0.5 cm from the actual source depth for all such cases. The artifact removal and very good depth location come at the expense of an impact on the signal to noise ratio (SNR) of the sources. For the strongest source and using the continuous detector the SNR increases unexpectedly to give values higher than that for observations made only in the critical plane due to the ghosting of this source in other planes at different depths. For all other cases there is a decrease in SNR which is more marked for finer plane separations and for weaker sources.