A variety of problems in both medical diagnostics and nondestructive testing of materials requires the reconstruction of a portion or cross section of an object without directly viewing its interior. Tomographic imaging techniques allow noninvasive/nondestructive studies which minimize patient trauma and cost in the medical domain, and reduce manufacturing and maintenance expenses for many industries by transforming external measurements into images of the interior of the patient or object. The established methods for computing tomographic images in common examples such as x-ray CT scanning are inadequate for difficult cases involving a shortage of data or great uncertainty in their precise values due to inherent error in measurements. For these problems, algorithms are needed which explicitly take into account the characteristics of the measurement errors as well as common behavior of the tissue or materials under study. Much improvement has resulted from statistical methods such as Bayesian tomographic estimation, but conventional estimation techniques, based on homogeneous random field models and fixed optimization strategies, seem to be approaching their limits of improvement. This project is developing three principal innovations to improve the capabilities of tomographic systems, with particular focus on three-dimensional applications: (1) nonhomogeneous image cross section models which allow spatially varying image characteristics to be accurately estimated using a simple multiscale estimation procedure; (2) fast nonlinear optimization algorithms for minimizing the nonquadratic functions that result from MAP estimation with nonGaussian prior models; (3) a novel approach to tomographic reconstruction based on nonlinear, non-iterative estimation from back projection data. This research is applicable to the full range of emission and transmission tomographic problems, with particular experimental focus on 3D medical emission tomography.
