Direct 3D-reconstruction from a single 2D-image obtained through a coded-aperture

Reconstructions in emission tomography at 511 keV have to address insufficient amount of data due to poor performances of detectors at such energy. SPECT with classic collimators is generally not adapted to acquire such images, unless a large open-fraction collimator is considered. In this paper we propose a novel configuration for direct 3D-reconstruction from a single 2D-planar non-parallel projection, that is a challenging and ill-posed problem. First, a coded aperture and a 2D-detector are simulated to define a model of the imaging system and to generate synthetic data. In order to address the absence of sufficient data support, 3D-objects that are synthesized stand in the near- field region, at just a few centimetres from the surface of the detector. This configuration maximises the geometrical efficiency and consequently enhances the amount of data contained in the unique observed image. Secondly, an accelerated ML-EM algorithm is used to reconstruct 3D-objects. The basis of our approach reflects the assumption that the inner-structure of the transition matrix used for modelling the system affects significantly the behaviour of ML-EM algorithm and the whole reconstructed spatial distribution. The transition matrix depends directly on the geometry of the collimator. The impact of this geometry on the structure of the transition matrix is studied. This paper shows that a small-size detector is able to perform a 3D-reconstruction of a small object standing in the near-field domain, from a single 2D-image. Reconstructed objects exhibit a good spatial resolution : two 5 mm-diameter cylinders with a centre-to-centre distance of 6 mm are clearly separated. Cylindrical shapes are well-preserved, although depth direction is deformed. Promising simulations demonstrate the extreme potentials of our approach.