Transmission tomographic image reconstruction using alternating minimization algorithms

Images reconstructed from transmission tomographic data are often contaminated with severe streaking artifacts when high-density objects are present among low-density material. The standard reconstruction algorithm, filtered back projection, assumes a linear model for the data. This approximation falters when high-density materials attenuate a large percentage of the X-ray photons, resulting in low-count data that are more affected by nonlinearities such as scatter, spectral hardening, and edge-gradient effects.; Our model incorporates these effects and the Poisson nature of the collected data. We seek to minimize the I-divergence between the measured data and their parameterized means. An alternating minimization (AM) algorithm was developed to produce a sequence of image estimates such that the resulting I-divergence sequence is monotonically nonincreasing. The images produced by this algorithm show greatly diminished streaking artifacts, but artifacts connecting pairs of high-density objects still remain; these streaks eventually fade, but only after several thousand algorithm iterations. These images are vastly improved in both quality and convergence rate if one incorporates into the objective function prior information about the high-density objects. A new AM algorithm results with which the pose of these objects is estimated while concurrently producing a sequence of images satisfying a set of constraints imposed by the known information. The algorithm finds a pose within 0.1 mm of the true pose and nearly eliminates the streaks in images produced from synthetic data.; Due to mismatches between real data and our model, the "known" constraints on the high-density objects are not always accurate, which leads again to image artifacts. Thus, the data affected by these objects can be viewed as "missing"; other examples of missing data include truncated projections and limited angular views. We reformulated the problem to account for these missing data, and developed new AM algorithms using expanded image and data spaces. Results show significant improvements, when compared to the previous AM algorithms, for both real and synthetic data.; These findings indicate that significant improvements are possible when forming tomographic images from data with high-density objects present or when objects are located outside the scanner's field of view.