Area weighted convolutional interpolation for data reprojection in single photon emission computed tomography

Abstract

A data reprojection algorithm has been developed for use in single photon emission computed tomography on an array processor equipped computer system. The algorithm makes use of an accurate representation of pixel activity (uniform square pixel model of intensity distribution), and is rapidly performed due to the efficient handling of an array-based algorithm and the fast Fourier transform on parallel processing hardware. The algorithm consists of using a pixel driven nearest-neighbor projection operation to an array of subdivided projection bins. The subdivided project bin array is then convolved with the angle-dependent projection of the area of a uniform square pixel and compressed to original bin size. The new algorithm has thus been named the area weighted convolution (AWC) method of interpolation. When compared to nearest-neighbor and linear interpolation algorithms, the new AWC algorithm was found to be more accurate, having an accuracy approaching that of the line length algorithm. It also yielded an easier and more efficient implementation on parallel hardware than line length or linear interpolation, with faster execution times than either.

Bandlimited and Haar filtered back-projection reconstructions

“…For these methods the entire scheme takes a discrete form and numerous approaches to express the discrete Radon operator in a consistent manner have already be attempted. Schwinger et al [5] have used the pixel shape to correct the reprojection step in SPECT and Schmidlin [6] has done the same for the PET implementation. Hanson and Wecksung [7] have defined local basis-functions (spline and truncated Gaussian) on a square grid to express the behavior of the continuous function within a small neighborhood.…”

Iterative image reconstruction for positron emission tomography: a study of convergence and quantitation problems

“…During reprojection and backprojection, a nearest-neighbour mapping was used into an N times more densely sampled intermediate projection. Then the final projections can be obtained by a convolution with a triangle [lo] or pixel area function [14]. The nearest-neighbour interpolation introduces an error which depends on the zoom factor N for the intermediate projections.…”

Iterative reconstruction of PET images using a high-overrelaxation single-projection algorithm

“…which may be calculated by the convolution method (Schwinger et al 1986): fine scale projection of the voxel centres along the LORs, convolution with the projected voxel profile, and finally recombination of the fine LORs. Some improvements have been implemented in this procedure (variable binning and abbreviated convolution; Schmidlin 1994).…”