Pattern Theory

required reading for any mathematician [involved] in the modeling complex and realistic signals
-Marco Loog, Nieuw Archief voor Wiskunde, December 2011

The book comes with a large number of exercises and problems, some requiring computer programming. Thanks to these, it can be used as a textbook to support a quite original course that could be offered by a department of applied mathematics, computer science or electrical engineering. In fact, this excellent book targets and deserves a broad readership. It will provide precious and interesting material to anyone who would like to discover pattern theory and how it traverses across geometry, probability and signal processing.
-Laurent Younes, Mathematical Reviews, Issue 2011m

... a masterpiece. It is one of the best books I have ever read. ... What singles out this outstanding book is an extremely original subject development. ... This book is so exciting. It is a detective fiction. It is an inquiry into 'real-world signals.' In contrast to most detective stories, the beauty of the style is exceptional and meets the standards of the best writers. Art and beauty are present everywhere in this marvelous book. ... The overall organisation of the book is also marvelous. ... The authors are leaders in signal and image processing and this book is based on their extremely innovative research. Reading this book is like entering David Mumford's office and beginning a friendly and informal scientific discussion with him and Agnes. That is a good approximation to paradise.
-Yves Meyer, EMS Newsletter, September 2011

Pattern Theory covers six classic attempts at modeling signals from the human and natural world: natural language (written), music, character recognition, texture modeling, face recognition, and natural scenes. These applications, appealing to students and researchers alike, include fourteen 'crash courses' giving all the needed basics, exercises, and numerical simulations. ... a complete pedagogic tool at master or first-year graduate level. I endorse the publication of Pattern Theory, and will actually use it and recommend it to other researchers.
-Jean-Michel Morel, CMLA

This book is fascinating. It develops a statistic approach to finding the patterns in the signals generated by the world. The style is lucid. I'm reminded of Mumford's exposition of Theta functions and Abelian varieties in his Tata lectures. The exposition is thorough. The authors provide the necessary mathematical tools allowing scientists to pursue an exciting subject. I've been running a seminar at MIT entitled 'New Opportunities for the Interactions of Mathematics and Other Disciplines' because I'm convinced that mathematics will move in surprising new directions. Pattern Theory, a decade's effort, is a prime example.
-I.M. Singer, Institute Professor, MIT