This book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a state-of-the-art in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective. The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also presented. Applications range for the reconstruction of noisy or blurred images, pattern and face recognition, to nonlinear approximation in strongly anisotropic contexts, and to the classification tools based on multifractal analysis. Read more... Tight frame based method for high-resolution image reconstruction / Jianfeng Cai ... [et al.] -- Greedy algorithms for adaptive triangulations and approximations / Albert Cohen -- The contribution of wavelets in multifractal analysis / Stephane Jaffard ... [et al.] -- Wavelet methods for image-based face recognition : A survey / Chaochun Liu and Daoqing Dai -- Hilbert-Huang transform : Its background, algorithms and applications / Lihua Yang