ABSTRACT
This chapter describes image reconstruction from noisy projections similar to those found in computed tomography. One of the conceptual difficulties with reconstructions from projections is that the projection space is defined in terms of coordinates, x′,θ, while the object and image spaces are defined in terms of coordinates, x,y. The back projected noise power spectral density function for a single projection angle is nonzero along a slice in the spatial frequency domain. The chapter considers linear, shift invariant reconstruction. Image reconstruction in the presence of noise can be implemented in the same way as reconstruction in the absence of noise. The Wiener filter provides the best linear, shift invariant, least mean square estimate of the object. For a particular application, this may or may not provide the best image. For example, it may be desirable to perform some edge enhancement or smoothing of the image of the object, particularly, when the goal is to present the object to the radiologist.
