Sparse Image and Signal Processing

Jean-Luc Starck is Senior Scientist at the Institute of Research into the Fundamental Laws of the Universe, Commissariat à l'énergie atomique, Saclay, France. He was awarded the 2022 Tycho Brahe Medal by the European Astronomical Society. His research interests include cosmology, weak lensing data, and statistical methods such as wavelets and other sparse representations of data. He has published over 200 papers in astrophysics, cosmology, signal processing, and applied mathematics, and is also author of three books. Fionn Murtagh has served in the Space Science Department of the European Space Agency for twelve years. He is a Fellow of both the International Association for Pattern Recognition and the British Computer Society, as well as an elected member of the Royal Irish Academy and of Academia Europaea. He is a member of the editorial boards of many journals, and has been editor-in-chief of the Computer Journal for more than ten years. Jalal M. Fadili has been full professor at Institut Universitaire de France since October 2013. His research interests include signal and image processing, statistics, optimization theory, and low-complexity regularization. He is a member of the editorial boards of several journals.

1. Introduction to the world of sparsity; 2. The wavelet transform; 3. Redundant wavelet transform; 4. Nonlinear multiscale transforms; 5. Multiscale geometric transforms; 6. Sparsity and noise removal; 7. Linear inverse problems; 8. Morphological diversity; 9. Sparse blind source separation; 10. Dictionary learning; 11. Three-dimensional sparse representations; 12. Multiscale geometric analysis on the sphere; 13. Compressed sensing; 14. This book's take-home message.