The world according to wavelets : the story of a mathematical technique in the making

Drawing on interviews with leading wavelet researchers in the USA and France, this book tells the story of the rise of the field. It attempts to make the subject accessible to the non-mathematical reader, without sacrificing precision. The material is organized so that the mathematical details can be assimilated at the reader's own pace. The main text is devoid of formulas and relates a story of people and ideas, while separate boxes and appendices contain intricate discussions for the more mathematically minded. This book, lovingly written and highly accessible, embraces the often unheralded notion that mathematics contains ideas that can, and deserve, to be communicated to a wider public - even if what is communicated is at the level of appreciation rather that practical knowledge. Put simply, it is a book about the wavelet transform, that strange and scientifically intriguing new method of encoding information with an abundance of practical applications. Drawing on interviews with leading wavelet researchers in the United States and France, it tells the story of the meteoric rise of this new field from its scattered beginnings a decade ago to its current status as a hot topic cutting across traditional scientific boundaries. But more than that, this book is a wonderfully successful attempt to entice the non-mathematical reader into formerly uncharted territory without sacrificing precision. The material is masterfully organized so mathematical details can be assimilated at one's own pace; the main text is devoid of formulas and relates a story of people and ideas, while separate boxes and appendices contain intricate discussions for the more mathematically adventurous. Barbara Burke Hubbard begins her examination of wavelets with the story of the development of Fourier analysis, the essential underpinning for telephones, x-ray machines, and computers. Without any dizzying technical or mathematical detail she describes the more recent, meteoric rise of wavelet analysis and its many practical applications. The second half of the book lucidly presents the mathematical formulas and details of wavelet analysis for those seeking a deeper understanding. In this second edition she includes a discussion of new medical and genetic applications such as mammography, heart disease, and fingerprints; recent technical developments; a more in-depth look at wavelet history and wavelet researchers; and an updated bibliography and list of software and web sites. Although wavelets represent a departure from Fourier analysis, they are also natural extension of it: the two languages clearly belong to the same family.