lift::haarpoly Class Reference

Inheritance diagram for lift::haarpoly:

[legend]Collaboration diagram for lift::haarpoly:

[legend]List of all members.

Public Member Functions
	haarpoly ()
void	forwardTrans (double[] vec)
void	inverseTrans (double[] vec)
Protected Member Functions
void	interp (double[] vec, int N, int direction)
Static Package Attributes
static final int	numPts = 4

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Detailed Description

Haar transform extended with a polynomial interpolation step

This wavelet transform extends the Haar transform with a polynomial wavelet function.

The polynomial wavelet uses 4-point polynomial interpolation to "predict" an odd point from four even point values.

This class extends the Haar transform with an interpolation stage which follows the predict and update stages of the Haar transform. The predict value is calculated from the even points, which in this case are the smoothed values calculated by the scaling function (e.g., the averages of the even and odd values).

The predict value is subtracted from the current odd value, which is the result of the Haar wavelet function (e.g., the difference between the odd value and the even value). This tends to result in large odd values after the interpolation stage, which is a weakness in this algorithm.

This algorithm was suggested by Wim Sweldens' tutorial Building Your Own Wavelets at Home.

  
  http://www.bearcave.com/misl/misl_tech/wavelets/lifting/index.html
  

Copyright and Use

You may use this source code without limitation and without fee as long as you include: <blockquote> This software was written and is copyrighted by Ian Kaplan, Bear Products International, www.bearcave.com, 2001. </blockquote>

This software is provided "as is", without any warrenty or claim as to its usefulness. Anyone who uses this source code uses it at their own risk. Nor is any support provided by Ian Kaplan and Bear Products International.

Please send any bug fixes or suggested source changes to:

     iank@bearcave.com

Author:

Ian Kaplan

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Constructor & Destructor Documentation

lift::haarpoly::haarpoly (   )  [inline]

haarpoly class constructor { fourPt = new polyinterp(); }

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Member Function Documentation

void lift::haarpoly::forwardTrans (  double[]  vec  )  [inline]

Haar transform extened with polynomial interpolation forward transform. This version of the forwardTrans function overrides the function in the liftbase base class. This function introduces an extra polynomial interpolation stage at the end of the transform. Reimplemented from lift::liftbase. { final int N = vec.length; for (int n = N; n > 1; n = n >> 1) { split( vec, n ); predict( vec, n, forward ); update( vec, n, forward ); interp( vec, n, forward ); } // for } // forwardTrans

void lift::haarpoly::interp (  double[]  vec, int  N, int  direction )  [inline, protected]

Predict an odd point from the even points, using 4-point polynomial interpolation. The four points used in the polynomial interpolation are the even points. We pretend that these four points are located at the x-coordinates 0,1,2,3. The first odd point interpolated will be located between the first and second even point, at 0.5. The next N-3 points are located at 1.5 (in the middle of the four points). The last two points are located at 2.5 and 3.5. For complete documentation see http://www.bearcave.com/misl/misl_tech/wavelets/lifting/index.html The difference between the predicted (interpolated) value and the actual odd value replaces the odd value in the forward transform. As the recursive steps proceed, N will eventually be 4 and then 2. When N = 4, linear interpolation is used. When N = 2, Haar interpolation is used (the prediction for the odd value is that it is equal to the even value). Parameters: vec  the input data on which the forward or inverse transform is calculated. N  the area of vec over which the transform is calculated direction  forward or inverse transform { int half = N >> 1; double d[] = new double[ numPts ]; int k = 42; for (int i = 0; i < half; i++) { double predictVal; if (i == 0) { if (half == 1) { // e.g., N == 2, and we use Haar interpolation predictVal = vec[0]; } else { fill( vec, d, N, 0 ); predictVal = fourPt.interpPoint( 0.5, half, d ); } } else if (i == 1) { predictVal = fourPt.interpPoint( 1.5, half, d ); } else if (i == half-2) { predictVal = fourPt.interpPoint( 2.5, half, d ); } else if (i == half-1) { predictVal = fourPt.interpPoint( 3.5, half, d ); } else { fill( vec, d, N, i-1); predictVal = fourPt.interpPoint( 1.5, half, d ); } int j = i + half; if (direction == forward) { vec[j] = vec[j] - predictVal; } else if (direction == inverse) { vec[j] = vec[j] + predictVal; } else { System.out.println("poly::predict: bad direction value"); } } } // interp

void lift::haarpoly::inverseTrans (  double[]  vec  )  [inline]

Haar transform extened with polynomial interpolation inverse transform. This version of the inverseTrans function overrides the function in the liftbase base class. This function introduces an inverse polynomial interpolation stage at the start of the inverse transform. Reimplemented from lift::liftbase. { final int N = vec.length; for (int n = 2; n <= N; n = n << 1) { interp( vec, n, inverse ); update( vec, n, inverse ); predict( vec, n, inverse ); merge( vec, n ); } } // inverseTrans

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The documentation for this class was generated from the following file:

• lift/haarpoly.java

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