Mathematics Colloquia and Seminars

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In medical or scientific applications, images are generally acquired with a specific task or set of tasks in mind. The goal of good design of imaging devices is to pack as much task-relevant information into the image data as possible. The role of image reconstruction, and image processing in general, is to make this information available to the end user. It is usually the case that the end user of a diagnostic imaging system is a human observer. Optimizing the transfer of diagnostic information to human observers implies some understanding of how the observers extract this information from the image. One way to assess information content in this context is through psychophysical studies where observer performance is evaluated on a battery of test images. Unfortunately, such studies are costly and time consuming, and hence not suitable for large-scale optimization of image reconstruction algorithms with many free parameters. These difficulties with human-observer studies have motivated the search for models of human-observer performance in diagnostic tasks. A large class of such models is based on first and second-order statistics (mean, variance, and covariance) of the images. For tomographic images, which have been reconstructed from projections, these statistical properties are determined by the manner in which noise in the raw projection data propagates through the image reconstruction algorithm. In this seminar, I will describe an approach to analyzing noise propagation through iterative reconstruction algorithms. The analysis motivates the development of "adjoint" iterative algorithms that implement the adjoint of the reconstruction operator (or the first-order adjoint for nonlinear algorithms). The approach is applied to the problem of finding an optimal stopping point for iterative algorithms in a simple detection task.

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