Resumen de Publicaciones

Wavelet

Otros

1989

A theory for multiresolution signal decomposition: the wavelet representation

S. Mallat

IEEE Transactions on Pattern Analysis and Machine Intelligence Vol 11, Nr0. 7,

198Jul. 1989, pp. 6p.674-693

Abstract :

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 studied. It is shown that the difference of information between the approximation of

a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted

by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the

vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a

wavelet orthonormal basis is a family of functions which is built by dilating and translating

a unique function psi (x). This decomposition defines an orthogonal multiresolution

representation called a wavelet representation. It is computed with a pyramidal algorithm

based on convolutions with quadrature mirror filters. Wavelet representation lies between

the spatial and Fourier domains. For images, the wavelet representation differentiates

several spatial orientations. The application of this representation to data compression in

image coding, texture discrimination and fractal analysis is discussed

1994

Multiresolution transient detection

Abry, P.; Flandrin, P.

Time-Frequency and Time-Scale Analysis, 1994., Proceedings of the IEEE-SP

International Symposium on , 1994

Page(s): 225 -228

Abstract :

Designs and studies the performance of a multiresolution-based transient detector. The

transients the authors are interested in consist of wide-band, pulse-like, coherent

structures in a turbulent flow. To take advantage of the fast pyramidal wavelet algorithm,

an important point when processing large amounts of experimental data, the detector

makes use of the discrete wavelet transform. The authors show how the lack of

time-invariance drawback of the discrete transform can be efficiently overcome by using

relevant analytic wavelets. They thus compare this detection technique with one based on

a continuous wavelet transform, as well as with other standard methods and show that

wavelets perform best when the transients are superimposed on a colored 1/f background

noise. This description is very close to that of turbulence and relevant also in many other

situations.

1996