Coded aperture design in compressive X-ray tomography

Coded aperture X-Ray tomography places a physical coded aperture in front of an X-ray source, the elements in the code either block or let an X-ray beam pass, which produces a patterned compressive projection onto the detector. Given several projections, compressed sensing (CS) reconstruction algorithms are then used to recover the three-dimensional object. The motivation to use coded apertures in this problem, is to reduce the number of measurements (projections) that in this case is equivalent to less radiation exposure to a patient. In this work, we consider the tomosynthesis problem, consisting of multiple X-ray sources which are placed over a three-dimensional data cube. The energy of each of the sources is modulated by a set of coded apertures. The projections are measured by a two-dimensional detector located below the object. Random coded apertures have been used before obtaining promising results. In this paper, the coded apertures are optimized using the generalized mapping of the cone beam energy onto the detector. In our scenario, the PSNR of the reconstructions images by using the optimized codes is up to 3 dB higher than those attained by the random coded apertures.