Tomographic Systems

3 units

The study of systems for imaging the interior of an object from external measurements. Mathematical preliminaries: multidimensional linear-systems, the Poisson process, maximum-likelihood estimation. Transmission, emission, reflection, and magnetic-resonance tomography. Line integral, strip integral, weighted-integral, and divergent-ray descriptions of tomographic data. The Radon transform. Reconstruction from ideal data: filtered back-project, back-project filter, Fourier, and inverse Radon-transform methods. Reconstruction from ideal data: filtered back-project, back-project filter, Fourier, and inverse Radon-transform methods. Reconstruction from blurred and noisy data: confidence-weighting, minimum-divergence deblurring, and estimation-based methods. Techniques for treatment of mission data, attenuation, and accidentals. Application to positron-emission, single-photon emission, x-ray, and magnetic-resonance tomography and to high resolution radar-imaging. Computer architectures for producing tomographic imagery.