Some results on the use of local basis functions for reconstruction representation in computed tomography

Abstract

In computed tomography (CT) as well as other areas of digital image processing, a discrete representation of a function of two variables on a continuous domain is needed. One approach is to specify the values of the function on an equally spaced grid and interpolate for intermediate values. A more general approach Is to represent the function as a linear combination of basis functions [1,2]. Iterative CT algorithms, e.g., ART, require repeated evaluation of line or strip projection integrals over a trial object function (reconstruction). If the first representation is selected, then we must get interpolated values in order to perform the integration. The interpolation can be performed in a variety of ways; each way makes implicit use of a set of basis functions. If nearest-neighbor interpolation is chosen, the resulting set of basis functions are square pixels centered on the sample points. For bilinear interpolation we get a bilinear tent function and for band-limited interpolation we get a product of separable sine functions with zeros at all sample points but one.