Wavelet transforms are recent mathematical techniques, based on group theory and square
integrable representations, which allows one to unfold a signal, or a field, into both space …

Sparse and redundant representation modeling of data assumes an ability to describe
signals as linear combinations of a few atoms from a pre-specified dictionary. As such, the …

The great response to the publication of my book Classical and Modern Fourier Analysis in
2004 has been especially gratifying to me. I was delighted when Springer offered to publish …

We construct orthonormal bases of compactly supported wavelets, with arbitrarily high
regularity. The order of regularity increases linearly with the support width. We start by …

Donoho and Johnstone (1994) proposed a method for reconstructing an unknown function f
on [0, 1] from noisy data d/sub i/= f (t/sub i/)+/spl sigma/z/sub i/, i= 0,..., n-1, t/sub i/= i/n, where …

Multiresolution representations are effective for analyzing the information content of images.
The properties of the operator which approximates a signal at a given resolution were …

Two different procedures for effecting a frequency analysis of a time-dependent signal
locally in time are studied. The first procedure is the short-time or windowed Fourier …

We attempt to recover a function of unknown smoothness from noisy sampled data. We
introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical …

Over the last two years, wavelet methods have shown themselves to be of considerable use
to harmonic analysts and, in particular, advances have been made concerning their …

Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those
parts of mathematics and its applications that use the struc ture of translations and …