New reconstruction algorithm, distance dependent exact, with reduced statistical α error, dedicated to emission tomography using a collimator with large and long holes

SPECT (single photon emission computerized tomography) is physically one of the worst medical imaging modalities. Despite a considerable and still increasing medical impact, its spatial resolution (beyond 1 cm) and its sensitivity (less than 10^-4) are both awful. This situation is mainly due to the use of a thin parallel hole collimator. In addition the application of the unfitted radon-transform worsens the figure. We already suggested a different approach of collimation called CACAO in French standing for computer aided collimation gamma camera. This approach uses a large and long hole collimator, a different sequence of acquisition with a linear scanning motion and a dedicated reconstruction program taking full account of the depth dependent response function. Up to now, however, the CACAO project has failed to convince the scientific community of its superiority over the conventional thin hole collimator. This is due of a lack of a good reconstruction algorithm. In this paper we depict a new tomographic reconstruction algorithm for the CACAO problem. In addition to the former cited advantages, this new algorithm is exact, it takes full account of the finite geometry of the collimator holes, it reduces the type 1 statistical error (false positive) and reduces the hindering effect of points with large errors (outliers). Example of reconstruction with exact data and with a limited number of detected photons are provided. Comparison with MLEM algorithm is provided.