In the past two decades, there have been extraordinary advances in both hardware and algorithms for computed tomography (CT). Despite the major advances, one component, the reconstruction algorithm, of CT scanners has remained virtually constant for the past 20 years. It is somewhat puzzling that fundamental advances in the solution of inverse problems, especially tomographic reconstruction, have not been translated into clinical and related practice. The reasons are not obvious and seldom discussed. In the presentation, I will examine some of the possible reasons for this discrepancy. Image reconstruction examples based upon both analytic and optimization-based approaches will be used for (1) elucidating the possible disconnect between theories and issues that arise in practical CT imaging and (2) demonstrating potentials of advanced algorithms to impact on CT and other applications, if the link between applied mathematicians and engineers/physicists were stronger.
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