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iowave1

$ \bigcirc$Name


iowave1 Reconstructs a signal from an orthogonal wavelet transform




$ \bigcirc$Command Synopsis


iowave1 [-r RecursNum] [-h HaarLevel] [-e EdgeMode] [-p PrecondMode] [-i] [-n FilterNorm] WavTrans RecompSignal ImpulseResponse [EdgeIR ]



-r RecursNum : Number of levels (default 1)

-h HaarLevel : Start reconstruction with Haar from HaarLevel

-e EdgeMode : Edge processing mode (0/1/2/3, default 3)

-p PrecondMode : Edge preconditionning mode (0/1/2, default 0)

-i : Invertible transform

-n FilterNorm : Filter taps normalization (0/1/2, default 2)

WavTrans : Input wavelet transform (wtrans1d)

RecompSignal : Reconstructed signal (fsignal)

ImpulseResponse : Impulse response of inner filters (fsignal)

EdgeIR : Impulse reponses of edge and preconditionning filters (fimage)




$ \bigcirc$Function Summary


void iowave1 (NumRec , Haar , Edge , Precond , Inverse , FilterNorm , Wtrans , Output , Ri , Edge_Ri )

int *NumRec ;

int *Haar ;

int *Edge ;

int *Precond ;

int *Inverse ;

int *FilterNorm ;

Wtrans1d Wtrans ;

Fsignal Output ;

Fsignal Ri ;

Fimage Edge_Ri ;




$ \bigcirc$Description


iowave1 reconstructs a signal from a sequence of sub-signals forming a wavelet decomposition, according to the pyramidal algorithm of S. Mallat [Mal89]. The notations that are used here have been already defined in owave1 module's documentation, and the reader is refered there to see their signification.

WavTrans is the prefix name of a sequence of files containing the coefficients of a wavelet decomposition AJ, DJ, DJ-1,..., D1. iowave1 computes A0, i.e. the inverse wavelet transform of WavTrans. As for the decomposition this is done recursively : Aj-1 is computed from Aj and Dj. Here again the one-step algorithm is very simple due to the two-scale relationship

$\displaystyle \sqrt{{2}}$ $\displaystyle \varphi$(2x) = $\displaystyle \sum_{{l}}^{}$hk-2l$\displaystyle \varphi$(x - l )+ $\displaystyle \sum_{{l}}^{}$gk-2l$\displaystyle \psi$(x - l )

And thus

Aj-1[k] = $\displaystyle \sum_{{l}}^{}$hk-2lAj[l] + $\displaystyle \sum_{{l}}^{}$gk-2lDj[l]

The edge processing methods are corresponding to those described for owave1.

The complexity of the algorithm is roughly the same as for owave1.

The sample values of the reconstructed signal are stored in the file RecompSignal.

The coefficients hk of the filter's impulse response are stored in the file ImpulseResponse. The coefficients of the filter's impulse response for computing the edge coefficients are stored in the file EdgeIR.




$ \bigcirc$See Also


precond1d, sconvolve.

stvrestore.


$ \bigcirc$Version 1.2


Last Modification date : Thu Jan 31 15:11:06 2002


$ \bigcirc$Author


Jean-Pierre D'Ales






next up previous contents index
Next: iowave2 Up: Reference Previous: ibiowave2   Contents   Index
mw 2004-05-05