Fast decoding algorithms are described for a number of established coded aperture systems. The fast decoding algorithms for all these systems offer significant reductions in the number of calculations required when reconstructing images formed by a coded aperture system and hence require less computation time to produce the images. The algorithms may therefore be of use in applications that require fast image reconstruction, such as near real-time nuclear medicine and location of hazardous radioactive spillage. Experimental tests confirm the efficacy of the fast decoding techniques.