LastWave

LastWave is a wavelet signal and image processing environment writ ten in C for X%Unix and Macintosh computers This standalone freeware does not require any additional commercial package and can be retrieved through the Internet at

http://www.cmap.polytechnique.fr/~bacry/LastWave/

LastWave was created and is maintained by Emmanuel Bacry at Ecole Polytechnique in France It includes a command line language and a high level objectoriented graphic language for displaying simple objects buttons strings and more complex ones signals images wavelet transforms timefrequency planes The computational sub routines and commands are regrouped in independent packages An extensive online documentation is available New commands are added with the command language or as C subroutines This software is rapidly evolving with packages provided by users across the Internet The current contributors include Benjamin Audit Geo Davis Nicolas Decoster J”erome Fraleu R”emi GribonvalWenLiang Hwang St”ephane Mallat Jean Francois Muzy and Sifen Zhong The following gives a list of current packages in bold with their main computational commands and the sections they relate to :

Signal  
s Arithmetic calculations over signals

fft Forward and inverse fast Fourier transforms

conv Fast convolution

Wavelet Transform 
1d 
cwt Continuous wavelet transform

owtd owtr Orthogonal and biorthogonal wavelet transforms forward and reverse

wthresh Wavelet coecient thresholding

Wavelet Transform Maxima 
1d
extrema chain Computes the maxima of a continuous wavelet transform and chains them through scales

Wavelet Transform Modulus Maxima Method 
1d
pf Computes the partition functions and singularity spectra of multifractal signals

Matching Pursuit

stftd Short time windowed Fourier transform

mp mpr Matching pursuit in a Gabor dictionary forward and reverse

Image 
i Arithmetic operations over images

Orthogonal Wavelet Transform  2d
owtd owtr Orthogonal and biorthogonal wavelet transforms of images forward and reverse

Dyadic Wavelet Transform  2d 
dwt2d , dwt2r Dyadic wavelet decomposition of images forward and reverse

extrema2 , extrecons2 Computes the modulus maxima of a dyadic wavelet transform and reconstructs the image from these maxima

chain2 Computes the chains of modulus maxima corresponding to edges

denoise2 Denoising by thresholding the chains of modulus maxima

Compression  2d 
code2 , decode2 Image compression with a wavelet transform code and reconstruction of the coded image