TABLE OF CONTENTS Image processing is an important application of Donoho's discoveries. This work concerns geometric-type images, and here is what it is about. A real image, like that of a classroom, is composed (approximately) of geometric forms that are outlined by rather simple contours. These geometric forms are "filled in" with variations in the luminous intensity called textures. For example, some students wear pullover sweaters, and a close examination of these sweaters reveals periodic, or almost periodic, patterns that have high spatial frequency with weak intensity. This is to say that the variations in luminous intensity may be very rapid but are weak when compared with the much more pronounced variations at the edges of the students' silhouettes. If we asked a talented draftsperson to make a sketch of this classroom, the lines representing the contours would be very distinct while the textures would be reproduced with much less fidelity. These textures, like those created by hair, would be suggested rather than carefully drawn. This is indeed how an artist works. For example, A. Durer was famous for being able to create, with a single brush stroke, hair that appeared to be drawn hair by hair.
Such ideas led to the concept of simulating natural textures automatically using algorithmic techniques that imitate D rer's brush. Currently, two-dimensional versions of fractional Brownian motion can be used to simulate some kinds of textures. These simulations are made by representing a fractional Brownian motion as a series of appropriate wavelets with i.i.d.
