ABSTRACT
This chapter focuses on stochastic images with a simple mathematical result of fundamental importance that finds frequent applications in the image processing area, namely, in image restoration. In medicine, color is mostly used only for emphasizing the contrast of originally gray-scale images via false colors or for labeling, neither usually using formally derived algorithms to determine the colors. In real-color image processing, although rarely appearing in medical applications, the images may be treated as vector valued, thus the correlation among the color components utilized. Although natural images are real valued, the generalization to the concept of complex-valued images is useful theoretically and may even simplify computations in some cases. The two-dimensional Fourier transform may be interpreted in terms of harmonic image components, similarly to its one-dimensional counterpart, which is interpreted in terms of harmonic signal components. Linear methods form a substantial part of image-processing methodology, and the corresponding theory is well elaborated.
