qccwavwaveletdwt1dint.3

spiht for linux this is used to decod and encode vedio i wich all enjoy

.TH QCCWAVWAVELETDWT1DINT 3 "QCCPACK" ""
.SH NAME
QccWAVWaveletDWT1DInt, QccWAVWaveletInverseDWT1DInt \- 
integer-valued discrete wavelet transform and inverse transform for a 1D signal
.SH SYNOPSIS
.B #include "libQccPack.h"
.sp
.BI "int QccWAVWaveletDWT1DInt(QccVectorInt " signal ", int " signal_length ", int " signal_origin ", int " subsample_pattern ", int " num_scales ", const QccWAVWavelet *" wavelet );
.br
.BI "int QccWAVWaveletInverseDWT1DInt(QccVectorInt " signal ", int " signal_length ", int " signal_origin ", int " subsample_pattern ", int " num_scales ", const QccWAVWavelet *" wavelet );
.SH DESCRIPTION
.B QccWAVWaveletDWT1DInt()
performs an integer-valued
discrete wavelet transform (DWT) of a one-dimensional signal.
.I num_scales
gives the number of scales, or levels, of the decomposition.
.BR QccWAVWaveletDWT1DInt()
implements a dyadic decomposition of
.IR signal ;
that is, the lowpass subband is recursively decomposed into lowpass and
highpass bands for each level of decomposition.
The transform is critically sampled; that is,
each subband produced in each decomposition level
has roughly half as many samples as the lowpass band of the preceding level.
The subbands output from the DWT are returned in
.IR signal ,
overwriting the original input signal.
The output subbands are nested in
.I signal
starting with the lowpass subband of the lowest (coarsest) level of
decomposition (i.e., the baseband) with subsequent highpass subbands
of increasing resolution following.
.LP
Essentially,
.BR QccWAVWaveletDWT1DInt()
calls
.BR QccWAVWaveletAnalysis1DInt (3)
for each level of decomposition;
.BR QccWAVWaveletAnalysis1DInt (3)
in turn calls
.BR QccWAVLiftingAnalysisInt (3).
.I signal_origin
indicates the sample index at which 
.I signal
starts.
.I wavelet
must indicate an integer-valued lifting scheme (see
.BR QccWAVLiftingSchemeInteger (3)).
.LP
.B QccWAVWaveletInverseDWT1DInt()
performs the inverse DWT of
.IR signal
which is assumed to have been produced
by
.BR QccWAVWaveletDWT1DInt() .
.I num_scales
gives the number of levels of decomposition that exist in
.IR signal .
Essentially,
.B QccWAVWaveletInverseDWT1DInt()
calls
.BR QccWAVWaveletSynthesis1DInt (3)
for each level of synthesis;
.BR QccWAVWaveletSynthesis1DInt (3)
in turn calls
.BR QccWAVFilterBankSynthesisInt (3).
.I signal_origin
indicates the sample index at which
.I signal
starts.
.LP
.I subsample_pattern
indicates the even- or odd-phase subsampling to be used at each level
of decomposition. In most applications, even subsampling at all
levels is desired, in which case
.I subsample_pattern
should be set to zero.
In more general settings, when some mixture of even- and odd-phase subsampling
is desired, 
.I subsample_pattern
can be an integer between 0 and
.RI "2^" num_levels " - 1."
In this integer, the 
.IR j th
bit (where
.I j
= 1 is the least-significant bit) indicates whether the
.IR j th
level of decomposition employs
even or odd subsampling (0 = even, 1 = odd).
For example, if
.I subsample_pattern
is 5, then the first and third decompositions use odd-phase
subsampling, while all others use even subsampling.
.SH "INTEGER-TO-INTEGER WAVELET TRANSFORMS"
Transforms generally provide perfect reconstruction in that the
inverse transform will perfectly invert transform coefficients
into an exact representation of the original signal.
However, when implemented in floating-point arithmetic, the potential
for loss arises due to the limits of finite precision in both the
forward and inverse transforms.
On the other hand,
transforms that map integer-valued signals into integer-valued
transforms coefficients can guarantee perfect reconstruction, provided
an inverse transform can be found.
For this reason, lifting schemes, in which inverse transforms are
trivial, are favored for the
implementation of integer-valued wavelet transforms. Typically,
the general approach proposed by Calderbank
.IR "et al" .
is followed wherein rounding of floating-point values to integers is performed
at each prediction and update step in a lifting scheme.
Integer versions of several popular biorthogonal wavelets were
created in this manner by Calderbank
.IR "et al" .,
as well as by Xiong
.IR "et al" .
.LP
In traditional floating-point lifting, the prediction and update steps
are generally followed by a single application of scaling by a constant
in order to produce the usual unitary normalization.
This scaling step is somewhat problematic for integer-valued lifting
since the scaling constant is usually not an integer.
In applications wherein unitary scaling is not required
(e.g., in some applications that process each subband completely
independently), the scaling step is simply dropped in order
to implement an integer-valued version of the transform.
Alternatively, one can append three additional lifting steps to 
implement the scaling; these additional lifting steps can then be rendered
integer-valued via appropriate rounding (e.g., Xiong
.IR "et al" .)
making the transforms approximately normalized.
This latter approach of scaling via additional lifting steps
is employed in the integer-valued
lifting schemes implemented in QccPack.
.SH "RETURN VALUES"
These routines
return 0 on success and 1 on error.
.SH "SEE ALSO"
.BR QccWAVWaveletAnalysis1DInt (3),
.BR QccWAVWaveletSynthesis1DInt (3),
.BR QccWAVLiftingAnalysisInt (3),
.BR QccWAVLiftingSynthesisInt (3),
.BR QccWAVWavelet (3),
.BR QccPackWAV (3),
.BR QccPack (3)
.LP
A. R. Calderbank, I. Daubechies, W. Sweldens, B.-L. Yeo, "Lossless
Image Compression Using Integer to Integer Wavelet Transforms", in
.IR "Proceedings of the International Conference on Image Processing" ,
Lausanne, Switzerland, pp. 596-599, September 1997.

Z. Xiong, X. Wu, S. Cheng, J. Hua, "Lossy-to-Lossless Compression of
Medical Volumetric Data Using Three-Dimensional Integer Wavelet Transforms,"
.IR "IEEE Transactions on Medical Imaging" ,
vol. 22, pp. 459-470, March 2003.

I. Daubechies and W. Sweldens,
"Factoring Wavelet Transforms Into Lifting Steps,"
.IR "J. Fourier Anal. Appl." ,
vol. 4, no. 3, pp. 245-267, 1998.
.SH AUTHOR
Copyright (C) 1997-2009  James E. Fowler
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