Images can be considered representative of random processes. Given the values of pixels in a well defined region, it is not possible to predict exactly the values of pixels outside of that region. For most images, it is likely that there is some relation between the pixel values inside and outside the known region, but the relationship is statistical. The fact that most images are the result of the measurement of radiation means that there is always some uncertainty about the exact value of a pixel, even within any known region. In fact, deterministic images are usually of little interest. From an information theoretic viewpoint, it is the uncertainty of the values of pixels that makes the information conveyed by the pixels important. This appendix will review the fundamentals that are assumed as a prerequisite for treating the various aspects of noise and stochastic models that are used in this text.

This appendix gives only brief definitions of the terms that we will use repeatedly in the text. It will only briefly discuss the elementary properties and concepts of stochastic processes that are necessary for the description of many of the imaging modeling processes discussed in the main text. Thus, this should be seen as a refresher of material that the reader has seen previously, or perhaps it indicates the material that the reader will need to learn from some more appropriate text in order to understand certain parts of this text.