Often, nowadays, one addresses public understanding of mathematics and rigor by pointing to important applications and how they underpin a great deal of science and engineering. In this context, multiple resolution methods in image and signal processing, as discussed in depth in this book, are important. Results of such methods are often visual. Results, too, can often be presented to the layperson in an easily understood way. In addition to those aspects that speak powerfully in favor of the methods presented here, the following is worth noting. Among the most cited articles in statistics and signal processing, one finds works in the general area of what we cover in this book.

The methods discussed in this book are essential underpinnings of data analysis, of relevance to multimedia data processing and to image, video, and signal processing. The methods discussed here feature very crucially in statistics, in mathematical methods, and in computational techniques.

Domains of application are incredibly wide, including imaging and signal processing in biology, medicine, and the life sciences generally; astronomy, physics, and the natural sciences; seismology and land use studies, as indicative subdomains from geology and geography in the earth sciences; materials science, metrology, and other areas of mechanical and civil engineering; image and video compression, analysis, and synthesis for movies and television; and so on.

There is a weakness, though, in regard to well-written available works in this area: the very rigor of the methods also means that the ideas can be very deep.