xyntific

xyntific is a fast lifting scheme impelementation of popular wavelet transforms (non dyadic DWT), written in low level C. This library is designed for non-dyadic data without resizing the input to dyadic length (i.e. powers of 2). Thus, non dyadic DWT can handle 39x39 images to maximum level, without intermediate buffering to 64x64.

Written and maintained by Omer Moussaffi ([email protected]). Published under GPL 3.0.

Data files are assumed to be headerless, so user should retain lists of sizes (cols/rows) for data files.

All wavelet transforms can be applied on any data size. Classical wavelet application is:

Data	a0	a1	a2	a3	a4	a5	...	a(2n-3)	a(2n-2)	a(2n-1)
Transform	low0	high1	low2	high3	low3	...	low(2n-4)	high(2n-3)	low(2n-2)	high(2n-1)
Pack	low0	low2	low4	...	low(2n-2)	high1	high3	high5	...	high(2n-1)

This implementation allows odd size data, and enables the transform to start from highpass. Perfect reconstruction is guaranteed as long as the user remembers to use the same boolean condition (startHigh = True/False) on the inverse transform. E.g.

Transform with startHigh = false (5 lowpass elements, 4 highpass elements):

Data	a0	a1	a2	a3	a4	a5	a6	a7	a8
Transform	low0	high1	low2	high3	low4	high5	low6	high7	low8
Pack	low0	low2	low4	low6	low8	high1	high3	high5	high7
Inverse	a0	a1	a2	a3	a4	a5	a6	a7	a8

or, Transform with startHigh = true (4 lowpass elements, 5 highpass elements):

Data	a0	a1	a2	a3	a4	a5	a6	a7	a8
Transform	high0	low1	high2	low3	high4	low5	high6	low7	high8
Pack	low1	low3	low5	low7	high0	high2	high4	high6	high8
Inverse	a0	a1	a2	a3	a4	a5	a6	a7	a8

Thus, for example, data of length 19 will have 10 highpass and 9 lowpass elements if startFroHigh is applied.

Implementation ispired by https://www.organicdesign.co.nz/Wavelet.c
Command line parameter parsing borrowed from James Fowler's QccPack (http://qccpack.sourceforge.net/).

Structure

When building, include upper library --libxyn.h--

general options for all executables:  
    -v verbose - display verbose information (mainly I/O)
    -type d|f|l|g|c - choose data type (integer|float|long|double exact|char). Currently, most functions support only d (integer), g (double) and f (float).  
    -length - integer length of data
    -fileName - input/output file name string  


genRandFile.c [-v ] [-type dataType] [-min min] [-max max] length fileName  
    generates a ranadom number vector, between $min and $max, of length $length and puts it into a file name $fileName.  


genLinearFile [-v ] [-type dataType] [-power power] [-min min] max len fileName  
    generates a polynomial file - y=a*x^n. $power is n (defualt 1), min and max are image min/max (def min=0)
    use these to test perfect reconstruction and statistical moments


calcMoment [-v ] [-type dataType] [-central ] [-divImp ] [-length len] moment inpName  
    calculate the n-th statistical moment on the data.  
    -cenrtal for central moment (remove mean from data)  
    -divImp calls an implementation dividing data inplace (diffenent rounding errors)  
    -length inputs only $len of the data  
    moment is the statistical moment order (=n).  
    non-central output is double = sum(data^n)/n. cantral output is sum((data-mean)^n)/n.  
    mean energy is non-central second moment.  


displayArray [-prec precision] [-digits digits] [-line lineLen] [-type  dataType(d|c|l|f|e)] [-length  len] fName
    displays the numeric contents of a binary file. 
    -prec is the number of dispayed fractional digits. Only relevant to floating point.
    -digits sets the spacde reserved for each number
    -line sets amount of numbers displayed per line.


displayWavelet [-lift ] waveName
    shows wavelet coefficients.
    -lift shows lifting coefficients
    waveNames supported: Haar, CDF-5-3, CDF-9-7


dwt1d/idwt1d [-v ] [-out outName] [-noscl ] [-type dataType] [-lift ] [-inPlace ] [-startHigh ] [-length len] waveName inpName
    -out output file name (default: inpName.fwd)
    -noscl - do not upscale integer data
    -lift call lifting implementation (usually better)
    -inPlace do not shuffle lowpass/highpass
    -startHigh - set first element of output to be highpass


dwt2d/idwt2d [-v ] [-out outName] [-type dataType] [-lift ] [-inPlace ] [-startHigh ] [-nC nC] nR waveName inpName
    seperable 2d wavelet transform - preform 1d transform and rows and cols
    -nC sets number of columns (default is calculated from filesize/nR)
    nR number of data rows