We have developed a model for transmission tomography that views the detected data as being Poisson-distributed photon counts. From this model, we derive an alternating minimization (AM) algorithm for the purpose of image reconstruction. This algorithm, which seeks to minimize an objective function (the I-divergence between the measured data and the estimated data), is particularly useful when high-density objects are present in soft tissue and standard image reconstruction algorithms fail. The approach incorporates inequality constraints on the pixel values and seeks to exploit known information about the high-density objects or other priors on the data. Because of the ill-posed nature of this problem, however, the noise and streaking artifacts in the images are not completely mitigated, even under the most ideal conditions, and some form of
regularization is required. We describe a sieve-based approach,
which constrains the image estimate to reside in a subset of the
image space in which all images have been smoothed with a Gaussian kernel. The kernel is spatially varying and does not smooth across known boundaries in the image. Preliminary results show effective reduction of the noise and streak artifacts, but indicate that more work is needed to suppress edge overshoots.