This book brings together the lectures given at the Les Houches summer school "Infrared space astronomy, today and tomorrow". It gives a wide overview of infrared astronomy, a wavelength domain crucial for studies of the solar system, stars at the beginning and end of their lives, interstellar matter and galaxies at all distances. Recent developments in observational techniques have been tremendous. The first contributions give an introduction to the basic physical processes and methods of detection and data processing. They are followed by a series of lectures dealing with the wide variety of astronomical objects that can be seen in the infrared.

How can we test if a supermassive black hole lies at the heart of every active galactic nucleus? What are LINERS, BL Lacs, N galaxies, broad-line radio galaxies and radio-quiet quasars and how do they compare? This timely textbook answers these questions in a clear, comprehensive and self-contained introduction to active galactic nuclei - for graduate students in astronomy and physics. The study of AGN is one of the most dynamic areas of contemporary astronomy, involving one fifth of all research astronomers. This textbook provides a systematic review of the observed properties of AGN across the entire electromagnetic spectrum, examines the underlying physics, and shows how the brightest AGN, quasars, can be used to probe the farthest reaches of the Universe. This book serves as both an entry point to the research literature and as a valuable reference for researchers in the field.

Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of these areas are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of time-frequency and time-scale methods as a rich area of work. "Foundations of Time-Frequency and Time-Scale Methods" will be suitable for applied mathematicians and engineers in signal/image processing and communication theory, as well as researchers and students in mathematical analysis, signal analysis, and mathematical physics.

The advancement of a scientific discipline depends not only on the "big heroes" of a discipline, but also on a community’s ability to reflect on what has been done in the past and what should be done in the future. This volume combines perspectives on both. It celebrates the merits of Michael Otte as one of the most important founding fathers of mathematics education by bringing together all the new and fascinating perspectives created through his career as a bridge builder in the field of interdisciplinary research and cooperation. The perspectives elaborated here are for the greatest part motivated by the impressing variety of Otte’s thoughts; however, the idea is not to look back, but to find out where the research agenda might lead us in the future. This volume provides new sources of knowledge based on Michael Otte’s fundamental insight that understanding the problems of mathematics education – how to teach, how to learn, how to communicate, how to do, and how to represent mathematics – depends on means, mainly philosophical and semiotic, that have to be created first of all, and to be reflected from the perspectives of a multitude of diverse disciplines.

Powerful techniques have been developed in recent years for the analysis of digital data, especially the manipulation of images. This book provides an in-depth introduction to a range of these innovative, avante-garde data-processing techniques. It develops the reader's understanding of each technique and then shows with practical examples how they can be applied to improve the skills of graduate students and researchers in astronomy, electrical engineering, physics, geophysics and medical imaging. What sets this book apart from others on the subject is the complementary blend of theory and practical application. Throughout, it is copiously illustrated with real-world examples from astronomy, electrical engineering, remote sensing and medicine. It also shows how many, more traditional, methods can be enhanced by incorporating the new wavelet and multiscale methods into the processing. For graduate students and researchers already experienced in image processing and data analysis, this book provides an indispensable guide to a wide range of exciting and original data-analysis techniques.