Preliminaries

This chapter reviews some mathematical concepts essential for understanding biomedical imaging principles. We first review commonly used special functions, functional spaces, and two integral transforms: the Fourier transform and the Radon transform.We then collect basic facts about the Moore-Penrose generalized inverse, singular value decomposition, and compact operators. The theory of regularization of ill-posed inverse problems is briefly discussed. The final section examines image characteristics with respect to various data acquisition and processing schemes. We focus specifically on issues related to image resolution, signal-to-noise ratio, and image artifacts.