MATRIX FORMULATION OF COMPUTED TOMOGRAM RECONSTRUCTION

Computed tomogram reconstruction theory is usually subdivided into two basic approaches: algebraic and analytic. Least-squares matrix formul ation provides a simple connection between these approaches. At this c onceptual level the dichotomy between the approaches reduces to choice of metric. The appropriate choice eliminates the matrix inversion imp licit in the algebraic methods and makes the correspondence to convolu tion backprojection clear. Additionally, the matrix formulation, by in corporating the features of a discrete, finite, overdetermined system, is much closer to actual computational implementations than the analy tic model. The analysis shows that non-linearities such as beam harden ing can be partially corrected for by the convolution. Using the matri x formulation we explore the effects of two commonly used backprojecti on interpolation schemes on the point spread function and the resultin g deviation from the continuous analytic model. From this perspective the continuous model can be viewed as a first-order approximation to t he exact least-squares discrete solution.