Math of Tomography

Signal processing and Fourier analysis fundamentals in one and several variables, deterministic algorithms for image reconstruction with non-diffracting sources, daling wiht noisy data and (briefly) the problem of diffracting sources, physically realistic statistical models for the data, the use of statistical parameter estimation as a reconstruction paradigm, likelihood maximization, the expectation maximization" (EM) iterative algorithm, applications of the EM algorithm to emission and transmission tomography, controlling noise through Bayesian "maximum a posteriori" estimation, and acceleration of convergence using incremental optimization or block-iterative methods.