Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour.… Expand

We show that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/Sup j/ can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/).Expand

The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions.Expand

The mathematical characterization of singularities with Lipschitz exponents of functions from the evolution across scales of their wavelet transform is reviewed.Expand

A Wavelet Tour of Signal Processing: The Sparse Way, third edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering.Expand

A multiresolution approximation is a sequence of embedded vector spaces V j jmember Z for approximating L 2 (R) functions. We study the properties of a multiresolution approximation and prove… Expand