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.
We propose an alternating minimization (AM) image estimation algorithm for iteratively reconstructing transmission tomography images. The algorithm is based on a model that accounts for much of the underlying physics, including Poisson noise in the measured data, beam hardening of polyenergetic radiation, energy dependence of the attenuation coefficients and scatter. It is well-known that these nonlinear phenomena can cause severe artifacts throughout the image when high-density objects are present in soft tissue, especially when using the conventional technique of filtered back projection (FBP). If we assume no prior knowledge of the high-density object(s), our proposed algorithm yields much improved images in comparison to FBP, but retains significant streaking between the high-density regions. When we incorporate the knowledge of the attenuation and pose parameters of the high-density objects into the algorithm, our simulations yield images with greatly reduced artifacts. To accomplish this, we adapted the algorithm to perform a search at each iteration (or after every n iterations) to find the optimal pose of the object before updating the image. The final iteration returns pose values within 0.1 millimeters and 0.01 degrees of the actual location of the high-density structures.