This thoroughly updated new edition presents state-of-the-art sparse and multiscale image and signal processing. It covers linear multiscale geometric transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Along with an up-to-the-minute description of required computation, it covers the latest results in inverse problem solving and regularization, sparse signal decomposition, blind source separation, in-painting, and compressed sensing. New chapters and sections cover multiscale geometric transforms for three-dimensional data (data cubes), data on the sphere (geo-located data), dictionary learning, and nonnegative matrix factorization. The authors wed theory and practice in examining applications in areas such as astronomy, including recent results from the European Space Agency's Herschel mission, biology, fusion physics, cold dark matter simulation, medical MRI, digital media, and forensics. MATLAB (R) and IDL code, available online at www.SparseSignalRecipes.info, accompany these methods and all applications.

The advent of advanced astronomical instruments and huge surveys means that the twenty-first century is witnessing a rapid growth in astrostatistical science. Interpreting the cosmic microwave background, weak and strong gravitational lensing, galaxy clustering and other signatures of the early Universe all require advanced statistical techniques. Led by members of the IAU's newly formed Working Group in Astrostatistics and Astroinformatics, IAU Symposium 306 emphasises the intricate mathematical methods needed to extract scientific insights from large and complicated datasets. It contains contributions on Bayesian methods, weak lensing cosmology, CMB data analysis, cross-correlating datasets, large-scale structure, data mining and machine learning, ongoing surveys and the future Euclid mission. The approaches presented here provide a solid foundation to advance new research methods in cosmology, making it an essential text for the large community of astronomers and statisticians who will analyse and interpret the vast and growing amount of observational data.

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, avant-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.