Matrix formulation of computed tomogram reconstruction

Computed tomogram reconstruction theory is usually subdivided into two basic approaches: algebraic and analytic. Least-squares matrix formulation provides a simple connection between these approaches. At this conceptual level the dichotomy between the approaches reduces to choice of metric. The appropriate choice eliminates the matrix inversion implicit in the algebraic methods and makes the correspondence to convolution backprojection clear. Additionally, the matrix formulation, by incorporating the features of a discrete, finite, overdetermined system, is much closer to actual computational implementations than the analytic model. The analysis shows that non-linearities such as beam hardening can be partially corrected for by the convolution. Using the matrix formulation the authors explore the effects of two commonly used backprojection interpolation schemes on the point spread function and the resulting deviation from the continuous analytic model.

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