TABLE OF CONTENTS The errors discussed in the last chapter are fundamental to the projection process and depend upon the interaction of object inhomogeneities with the form of energy used. The effects of these errors can t be lessened by simply increasing the number of measurements in each projection or the total number of projections.
This chapter will focus on reconstruction errors of a different type: those caused either by insufficiency of data or by the presence of random noise in the measurements. An insufficiency of data may occur either through undersampling of projection data or because not enough projections are recorded. The distortions that arise on account of insufficiency of data are usually called the aliasing distortions. Aliasing distortions may also be caused by using an undersampled grid for displaying the reconstructed image.
We will discuss aliasing from two points of view. First we will assume point sources and detectors and show the artifacts due to aliasing. With this assumption it is easy to show the effects of undersampling a projection, using too small a number of views, and choosing an incorrect reconstruction grid or filter. We will then introduce detectors and sources of nonzero width and discuss how they in effect help reduce the severity of aliasing distortions.
Fig. 5.1 shows 16 parallel beam reconstructions of an ellipse with various values of K, the number of projections, and N , the number of rays in each projection. The projections for the...
