Akram Aldroubi & Carlos Cabrelli 
New Trends in Applied Harmonic Analysis 
Sparse Representations, Compressed Sensing, and Multifractal Analysis

This volume is a selection of written notes corresponding to courses taught at the CIMPA School: ‘New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis’. New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to Ph D students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.

Mục lục

Multifractal Analysis of Cantor-like Measures.- Multifractal Analysis and Wavelets.- An Introduction to Mandelbrot Cascades.- Lebesgue-type Inequalities for Greedy Approximation.- Results on Non-linear Approximation for Wavelet Bases in Weighted Function Spaces.- Consequences of the Marcus/Spielman/Srivastava Solution of the Kadison-Singer Problem.- Model Sets and New Versions pf Shannon Sampling Theorem.- Stylometry and Mathematical Study of Authorship.- Thoughts on Numerical and Conceptual Harmonic Analysis.