Sparse image and signal processing : wavelets, curvelets, morphological diversity / Jean-Luc Starck, Fionn Murtagh, Jalal M. Fadili

This monograph presents a comprehensive survey of sparse representations and multiscale techniques in image and signal processing. The aim of the authors is to provide a bridge between theoretical background and easily applicable experimentation. This approach is based on a great deal of practical engagement across many application areas. This book weds theory and practice in examining applications in various areas such as astronomy, biology, physics, digital media, and forensics.

This book consists of 11 chapters, a comprehensive bibliography (with 462 references), and a subject index. Chapter 1 gives an introduction to sparse representations of signals and images. In the Chapters 2 – 5, the authors sketch main results of the computational harmonic analysis. Here they discuss linear multiscale transforms, such as wavelet, ridgelet, and curvelet transforms, as well as nonlinear multiscale transforms based on the median and mathematical morphology operators. In the Chapters 6 – 10, the concepts of sparsity and morphological diversity are exploited for various problems such as denoising, regularization of linear inverse problems, sparse signal decomposition, blind source separation, and multiscale geometric analysis on the sphere. The concept of morphological diversity is introduced to model a signal as a sum, where each summand is sparse in a given dictionary. For instance, by combining the Fourier and wavelet dictionaries, one can well represent signals that contain both stationary and localized features. The final Chapter 11 is devoted to the new sampling theory, compressed sensing, which provides an alternative to the known Shannon sampling theory. Compressed sensing uses the prior knowledge that signals are sparse, whereas Shannon theory was designed for bandlimited signals.

Each chapter contains a section on guided numerical experiments. The reader can find MATLAB programs, special images and signals on the website http://www.SparseSignalRecipes.info. This very useful book is mainly written for graduate students and researchers, who are interested in modern applications of computational harmonic analysis in image and signal processing. (zbMath)

Bibliogr. p. 289-309. Index