Maarten Jansen – författare

This book discusses statistical applications of wavelet theory for use in signal and image processing. The emphasis is on smoothing by wavelet thresholding and extended methods. Wavelet thresholding is an example of non-linear and non-parametric smoothing. The first part discusses theoretical and practical issues concerned with minimum risk thresholding and fast threshold estimation, using generalized cross validation. The extensions in later chapters consider possibilities to exploit three key properties of wavelets in statistics: sparsity, multiresolution, and locality. The author discusses original contributions to problems of correlated noise, scale dependent processing, Bayesian algorithms with geometrical priors (Markov random fields), non-equispaced data, and many other extensions. The point of view lies on the bridge between statistics, signal and image processing, and approximation theory, and the book is accessible for researchers from all of these fields. Most of the material has in mind applications in signal or image processing, and signals and images are used extensively in the illustrations.Nevertheless, the algorithms are quite general in the sense that they could also serve in other regression problems. The book also pays attention to fast algorithms, and Matlab code reproducing many of the illustrations is available for free. Maarten Jansen received a Ph.D. in applied mathematics from the Katholieke Universiteit Leuven, Belgium, in 2000 and currently he is a postdoctoral fellow with the Belgian Foundation for Scientific Research (FWO). He has been a visiting researcher at several institutes, including Stanford University, Bristol University, and Rice University.

The Mixtec, or the people of Nuu Savi (Nation of the Rain God), one of the major civilizations of ancient Mesoamerica, made their home in the highlands of Oaxaca, where they resisted both Aztec military expansion and the Spanish conquest. In 'Encounter with the Plumed Serpent', two leading scholars present and interpret the sacred histories narrated in the Mixtec codices, the largest surviving collection of pre-Columbian manuscripts in existence. In these screenfold books, ancient painter-historians chronicled the politics of the Mixtec from approximately ad900 to 1521, portraying the royal families, rituals, wars, alliances, and ideology of the times. By analysing and cross-referencing the codices, which have been fragmented and dispersed in far-flung archives, the authors attempt to reconstruct Mixtec history. Their synthesis here builds on long examination of the ancient manuscripts. Adding useful interpretation and commentary, Jansen and Perez Jimenez synthesise the large body of surviving documents into the first unified narrative of Mixtec sacred history.

Wavelets from a Statistical Perspective offers a modern, 2nd generation look on wavelets, far beyond the rigid setting of the equispaced, dyadic wavelets in the early days. With the methods of this book, based on the lifting scheme, researchers can set up a wavelet or another multiresolution analysis adapted to their data, ranging from images to scattered data or other irregularly spaced observations. Whereas classical wavelets stand a bit apart from other nonparametric methods, this book adds a multiscale touch to your spline, kernel or local polynomial smoothing procedure, thereby extending its applicability to nonlinear, nonparametric processing for piecewise smooth data.One of the chapters of the book constructs B-spline wavelets on nonequispaced knots and multiscale local polynomial transforms. In another chapter, the link between wavelets and Fourier analysis, ubiquitous in the classical approach, is explained, but without being inevitable. In further chapters the discrete wavelet transform is contrasted with the continuous version, the nondecimated (or maximal overlap) transform taking an intermediate position. An important principle in designing a wavelet analysis through the lifting scheme is finding the right balance between bias and variance. Bias and variance also play a crucial role in the nonparametric smoothing in a wavelet framework, in finding well working thresholds or other smoothing parameters. The numerous illustrations can be reproduced with the online available, accompanying software. The software and the exercises can also be used as a starting point in the further exploration of the material.

Wavelets from a Statistical Perspective offers a modern, 2nd generation look on wavelets, far beyond the rigid setting of the equispaced, dyadic wavelets in the early days. With the methods of this book, based on the lifting scheme, researchers can set up a wavelet or another multiresolution analysis adapted to their data, ranging from images to scattered data or other irregularly spaced observations. Whereas classical wavelets stand a bit apart from other nonparametric methods, this book adds a multiscale touch to your spline, kernel or local polynomial smoothing procedure, thereby extending its applicability to nonlinear, nonparametric processing for piecewise smooth data.One of the chapters of the book constructs B-spline wavelets on nonequispaced knots and multiscale local polynomial transforms. In another chapter, the link between wavelets and Fourier analysis, ubiquitous in the classical approach, is explained, but without being inevitable. In further chapters the discrete wavelet transform is contrasted with the continuous version, the nondecimated (or maximal overlap) transform taking an intermediate position. An important principle in designing a wavelet analysis through the lifting scheme is finding the right balance between bias and variance. Bias and variance also play a crucial role in the nonparametric smoothing in a wavelet framework, in finding well working thresholds or other smoothing parameters. The numerous illustrations can be reproduced with the online available, accompanying software. The software and the exercises can also be used as a starting point in the further exploration of the material.

In Time and the Ancestors: Aztec and Mixtec Ritual Art, Maarten Jansen and Aurora Pérez present new interpretations of enigmatic masterpieces from ancient Mexico. Combining iconographical analysis with the study of archaeological contexts, historical sources and living cultural traditions, they shed light on central symbols and values of the religious heritage of indigenous peoples, paying special attention to precolonial perceptions of time and the importance of ancestor worship. They decipher the meaning of the treasure deposited in Tomb 7 at Monte Albán (Oaxaca) and of artworks such as the Roll of the New Fire (Selden Roll), the Aztec religious sculptures and, last but not least, the mysterious chapter of temple scenes from the Book of Night and Wind (Codex Borgia).