java.lang.Object
- java.lang.Thread
- - gov.nih.mipav.model.algorithms.AlgorithmBase
  - - gov.nih.mipav.model.algorithms.filters.AlgorithmWaveletThreshold

All Implemented Interfaces:

java.awt.event.ActionListener, java.awt.event.WindowListener, java.lang.Runnable, java.util.EventListener
```
public class AlgorithmWaveletThreshold
extends AlgorithmBase
```
In hard thresholding a wavelet coefficient whose magnitude is below the product of threshold and the maximum wavelet magnitude is zeroed, and a wavelet coefficient whose magnitude is greater than or equal to the product is left unchanged. In soft thresholding a wavelet coefficient whose magnitude is below the product of threshold and the maximum wavelet magnitude is zeroed, and a wavelet coefficient whose magnitude is greater than or equal to the product has its magnitude decreased by the product. Generally, soft thresholding is a better choice. The signal reconstructed with the coefficients left after hard thresholding may have undesirable artifacts including sidelobes. Then, an inverse wavelet transform is performed. The image is stripped down to its original size. The data is clamped so as not to exceed the bounds of the data type of the image into which it is imported. This is a simple method of reducing white noise.

The forward and inverse Daubechies wavelet transform routines are taken from Numerical Recipes in C The Art of Scientific Computing, 2nd edition, by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Cambridge University Press, 1997, Chapter 13.10, pp. 591 - 606. The wavelet routines daub4, pwt, wt1, wtn, and pwtset in Numerical Recipes in C are in the public domain. See {@link http://www.nr.com/public-domain.html} for more information.

The wavelet transform is mathematically defined only within a signal; image applications need to solve the boundary problem. 4 different techniques exist:
1. Mirror image replication
2. Zero padding
3. Linear extrapolation
4. Circular convolution
In this module zero padding is used. As stated in the Medx 3.4 User's Guide in Chapter 17 on Advanced Image Processing Techniques: "The mirror condition can only be used with symmetric wavelet basis." "Daubechies wavelet bases are non-symmetrical orthogonal wavelets with compact support and are good for data suppression. Only the periodic boundary condition should be used when using the Daubechies wavelet basis." In Empirical Evaluation of Boundary Policies for Wavelet-based Image Coding by Claudia Schremmer zero padding, circular convolution, and mirror image padding are compared. She concludes that mirror padding works best with regard to quality, zero padding performs worst with regard to quality, and circular convolution is midway between the 2. The matlab wavelet toolbox literature says that "the disadvantage of zero padding is that discontinuities are artificially created at the border." Mirror padding "has the disadvantage of artificially creating discontinuities of the first derivative at the border, but this method works well in general for images." Extrapolation "works well in general for smooth signals." The wavelet toolbox uses mirror padding as its default mode. How much padding is required? Claudia Schremmer states: "With padding, the coefficients of the signal on either side of the border are padded with filter_length - 2 coefficients. Consequently, each signal coefficient enters into filter_length/2 calculations of convolution, and the transform is reversible."

The image is expanded so that all dimensions are powers of 2 and there is zero padding going past each original boundary by the coefficient number - 2. The image is transformed into wavelet coefficients.

Nested Class Summary
- Nested classes/interfaces inherited from class java.lang.Thread
  java.lang.Thread.State, java.lang.Thread.UncaughtExceptionHandler

Field Summary

Fields
Modifier and Type	Field	Description
`private float[]`	`aArray`	DOCUMENT ME!
`private float`	`aCutoff`	DOCUMENT ME!
`private float[]`	`aExp`	DOCUMENT ME!
`private float[]`	`aLog`	DOCUMENT ME!
`private float`	`aMax`	DOCUMENT ME!
`private int`	`arrayLength`	DOCUMENT ME!
`private int`	`belowThreshold`	DOCUMENT ME!
`static double`	`C0`	coefficents for DAUB4 wavelet filter.
`static double`	`C1`	DOCUMENT ME!
`static double[]`	`c12`	DOCUMENT ME!
`static double`	`C2`	DOCUMENT ME!
`static double[]`	`c20`	DOCUMENT ME!
`static double`	`C3`	DOCUMENT ME!
`static double[]`	`c4`	coefficients for the PWT filter.
`private double[]`	`cc`	DOCUMENT ME!
`private int`	`cm2`	DOCUMENT ME!
`private int`	`cNum`	DOCUMENT ME!
`private double[]`	`cr`	DOCUMENT ME!
`private int`	`dataType`	DOCUMENT ME!
`static int`	`DAUB4`	underlying wavelet filter For 4 coefficients the routine daub4 is considerably faster than pwt.
`private boolean`	`doWaveletImage`	DOCUMENT ME!
`private int[]`	`extents`	DOCUMENT ME!
`private int`	`filterType`	DOCUMENT ME!
`static int`	`FORWARD`	DOCUMENT ME!
`private boolean`	`foundSize`	DOCUMENT ME!
`static int`	`HARD`	thresholding estimator.
`static int`	`INVERSE`	FORWARD and INVERSE are 2 possible transformDir values
`private int`	`ioff`	DOCUMENT ME!
`private int`	`joff`	DOCUMENT ME!
`private int`	`minSize`	DOCUMENT ME!
`private int`	`nDims`	DOCUMENT ME!
`private int`	`newArrayLength`	DOCUMENT ME!
`private int[]`	`newExtents`	DOCUMENT ME!
`private int`	`newXDim`	DOCUMENT ME!
`private int`	`newXY`	DOCUMENT ME!
`private int`	`newYDim`	DOCUMENT ME!
`private int`	`newZDim`	DOCUMENT ME!
`static int`	`NONNEGATIVE_GARROTE`
`private int`	`offsetX`	DOCUMENT ME!
`private int`	`offsetY`	DOCUMENT ME!
`private int`	`offsetZ`	DOCUMENT ME!
`static int`	`PWT`	DOCUMENT ME!
`static int`	`SCAD`
`static int`	`SOFT`	DOCUMENT ME!
`private float`	`threshold`	DOCUMENT ME!
`private int`	`thresholdType`	DOCUMENT ME!
`private int`	`transformDir`	DOCUMENT ME!
`private ModelImage`	`waveletImage`	DOCUMENT ME!
`private int`	`xDim`	DOCUMENT ME!
`private int`	`xy`	DOCUMENT ME!
`private int`	`yDim`	DOCUMENT ME!
`private int`	`zDim`	DOCUMENT ME!

Fields inherited from class gov.nih.mipav.model.algorithms.AlgorithmBase
destFlag, destImage, image25D, mask, maxProgressValue, minProgressValue, multiThreadingEnabled, nthreads, progress, progressModulus, progressStep, runningInSeparateThread, separable, srcImage, threadStopped

Fields inherited from class java.lang.Thread
MAX_PRIORITY, MIN_PRIORITY, NORM_PRIORITY

Constructor Summary

Constructors
Constructor	Description
`AlgorithmWaveletThreshold(ModelImage srcImg, int filterType, int cNum, int thresholdType, float threshold, boolean doWaveletImage)`	Creates a new AlgorithmWaveletThreshold object.
`AlgorithmWaveletThreshold(ModelImage destImg, ModelImage srcImg, int filterType, int cNum, int thresholdType, float threshold, boolean doWaveletImage)`	Creates a new AlgorithmWaveletThreshold object.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`private void`	`daub4(float[] a, int n)`	DOCUMENT ME!
`void`	`finalize()`	Prepare this class for destruction.
`ModelImage`	`getWaveletImage()`	Accessor that returns the image.
`private void`	`pwt(float[] a, int n)`	DOCUMENT ME!
`void`	`runAlgorithm()`	Starts the program.
`private void`	`wt1(float[] a)`	DOCUMENT ME!
`private void`	`wtn(float[] a)`	DOCUMENT ME!

Methods inherited from class gov.nih.mipav.model.algorithms.AlgorithmBase
actionPerformed, addListener, addProgressChangeListener, calculateImageSize, calculatePrincipleAxis, computeElapsedTime, computeElapsedTime, convertIntoFloat, delinkProgressToAlgorithm, delinkProgressToAlgorithmMulti, displayError, errorCleanUp, fireProgressStateChanged, fireProgressStateChanged, fireProgressStateChanged, fireProgressStateChanged, fireProgressStateChanged, generateProgressValues, getDestImage, getElapsedTime, getMask, getMaxProgressValue, getMinProgressValue, getNumberOfThreads, getProgress, getProgressChangeListener, getProgressChangeListeners, getProgressModulus, getProgressStep, getProgressValues, getSrcImage, isCompleted, isImage25D, isMultiThreadingEnabled, isRunningInSeparateThread, isThreadStopped, linkProgressToAlgorithm, linkProgressToAlgorithm, makeProgress, notifyListeners, removeListener, removeProgressChangeListener, run, setCompleted, setImage25D, setMask, setMaxProgressValue, setMinProgressValue, setMultiThreadingEnabled, setNumberOfThreads, setProgress, setProgressModulus, setProgressStep, setProgressValues, setProgressValues, setRunningInSeparateThread, setSrcImage, setStartTime, setThreadStopped, startMethod, windowActivated, windowClosed, windowClosing, windowDeactivated, windowDeiconified, windowIconified, windowOpened

Methods inherited from class java.lang.Thread
activeCount, checkAccess, clone, countStackFrames, currentThread, dumpStack, enumerate, getAllStackTraces, getContextClassLoader, getDefaultUncaughtExceptionHandler, getId, getName, getPriority, getStackTrace, getState, getThreadGroup, getUncaughtExceptionHandler, holdsLock, interrupt, interrupted, isAlive, isDaemon, isInterrupted, join, join, join, onSpinWait, resume, setContextClassLoader, setDaemon, setDefaultUncaughtExceptionHandler, setName, setPriority, setUncaughtExceptionHandler, sleep, sleep, start, stop, suspend, toString, yield

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Field Detail
  - INVERSE
```
public static final int INVERSE
```
    FORWARD and INVERSE are 2 possible transformDir values
    
    See Also:
    
    Constant Field Values
  - FORWARD
```
public static final int FORWARD
```
    DOCUMENT ME!
    
    See Also:
    
    Constant Field Values
  - DAUB4
```
public static final int DAUB4
```
    underlying wavelet filter For 4 coefficients the routine daub4 is considerably faster than pwt. DAUB4 implements a Daubechies 4-coefficient wavelet filter. PWT implements Daubechies filters with 4, 12, and 20 coefficients. DAUB4 and PWT use different default centerings. In spite of the faster speed of DAUB4, the dialog is designed only to call PWT so that the user only sees changes due to the number of coefficients and is not confused by changes in centering. Reference on NONNEGATIVE_GARROTE and SCAD thresholding: "Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study" by Anestis Antoniadis, Jeremie Bigot, and Theofanis Sapatinas, Journal of Statistical Software, Vol. 6, Issue 6, pp. 1-83, 2001.
    
    See Also:
    
    Constant Field Values
  - PWT
```
public static final int PWT
```
    DOCUMENT ME!
    
    See Also:
    
    Constant Field Values
  - C0
```
public static final double C0
```
    coefficents for DAUB4 wavelet filter.
    
    See Also:
    
    Constant Field Values
  - C1
```
public static final double C1
```
    DOCUMENT ME!
    
    See Also:
    
    Constant Field Values
  - C2
```
public static final double C2
```
    DOCUMENT ME!
    
    See Also:
    
    Constant Field Values
  - C3
```
public static final double C3
```
    DOCUMENT ME!
    
    See Also:
    
    Constant Field Values
  - c4
```
public static final double[] c4
```
    coefficients for the PWT filter.
  - c12
```
public static final double[] c12
```
    DOCUMENT ME!
  - c20
```
public static final double[] c20
```
    DOCUMENT ME!
  - HARD
```
public static final int HARD
```
    thresholding estimator.
    
    See Also:
    
    Constant Field Values
  - SOFT
```
public static final int SOFT
```
    DOCUMENT ME!
    
    See Also:
    
    Constant Field Values
  - NONNEGATIVE_GARROTE
```
public static final int NONNEGATIVE_GARROTE
```
    See Also:
    
    Constant Field Values
  - SCAD
```
public static final int SCAD
```
    See Also:
    
    Constant Field Values
  - aArray
```
private float[] aArray
```
    DOCUMENT ME!
  - aCutoff
```
private float aCutoff
```
    DOCUMENT ME!
  - aExp
```
private float[] aExp
```
    DOCUMENT ME!
  - aLog
```
private float[] aLog
```
    DOCUMENT ME!
  - aMax
```
private float aMax
```
    DOCUMENT ME!
  - arrayLength
```
private int arrayLength
```
    DOCUMENT ME!
  - belowThreshold
```
private int belowThreshold
```
    DOCUMENT ME!
  - cc
```
private double[] cc
```
    DOCUMENT ME!
  - cm2
```
private final int cm2
```
    DOCUMENT ME!
  - cNum
```
private final int cNum
```
    DOCUMENT ME!
  - cr
```
private double[] cr
```
    DOCUMENT ME!
  - dataType
```
private int dataType
```
    DOCUMENT ME!
  - doWaveletImage
```
private final boolean doWaveletImage
```
    DOCUMENT ME!
  - extents
```
private int[] extents
```
    DOCUMENT ME!
  - filterType
```
private final int filterType
```
    DOCUMENT ME!
  - foundSize
```
private boolean foundSize
```
    DOCUMENT ME!
  - ioff
```
private int ioff
```
    DOCUMENT ME!
  - joff
```
private int joff
```
    DOCUMENT ME!
  - minSize
```
private int minSize
```
    DOCUMENT ME!
  - nDims
```
private int nDims
```
    DOCUMENT ME!
  - newArrayLength
```
private int newArrayLength
```
    DOCUMENT ME!
  - newExtents
```
private int[] newExtents
```
    DOCUMENT ME!
  - newXDim
```
private int newXDim
```
    DOCUMENT ME!
  - newYDim
```
private int newYDim
```
    DOCUMENT ME!
  - newZDim
```
private int newZDim
```
    DOCUMENT ME!
  - offsetX
```
private int offsetX
```
    DOCUMENT ME!
  - offsetY
```
private int offsetY
```
    DOCUMENT ME!
  - offsetZ
```
private int offsetZ
```
    DOCUMENT ME!
  - threshold
```
private final float threshold
```
    DOCUMENT ME!
  - thresholdType
```
private final int thresholdType
```
    DOCUMENT ME!
  - transformDir
```
private int transformDir
```
    DOCUMENT ME!
  - waveletImage
```
private ModelImage waveletImage
```
    DOCUMENT ME!
  - xDim
```
private int xDim
```
    DOCUMENT ME!
  - yDim
```
private int yDim
```
    DOCUMENT ME!
  - zDim
```
private int zDim
```
    DOCUMENT ME!
  - xy
```
private int xy
```
    DOCUMENT ME!
  - newXY
```
private int newXY
```
    DOCUMENT ME!
- Constructor Detail
  - AlgorithmWaveletThreshold
```
public AlgorithmWaveletThreshold(ModelImage srcImg,
                                 int filterType,
                                 int cNum,
                                 int thresholdType,
                                 float threshold,
                                 boolean doWaveletImage)
```
    Creates a new AlgorithmWaveletThreshold object.
    
    Parameters:
    
    srcImg - source image model
    
    filterType - wavelet filter
    
    cNum - number of coefficients in the pwt filter
    
    thresholdType - HARD or SOFT thresholding
    
    threshold - fraction of maximum magnitude below which coefficients are zeroed
    
    doWaveletImage - display wavelet transform image in log magnitude if true
    
    userInterface - DOCUMENT ME!
  - AlgorithmWaveletThreshold
```
public AlgorithmWaveletThreshold(ModelImage destImg,
                                 ModelImage srcImg,
                                 int filterType,
                                 int cNum,
                                 int thresholdType,
                                 float threshold,
                                 boolean doWaveletImage)
```
    Creates a new AlgorithmWaveletThreshold object.
    
    Parameters:
    
    destImg - image model where result image is to be stored
    
    srcImg - source image model
    
    filterType - wavelet filter
    
    cNum - number of coefficients in the pwt filter
    
    thresholdType - HARD or SOFT thresholding
    
    threshold - fraction of maximum magnitude below which coefficients are zeroed
    
    doWaveletImage - display log maagnitude wavelet transform image if true
    
    userInterface - DOCUMENT ME!
- Method Detail
  - finalize
```
public void finalize()
```
    Prepare this class for destruction.
    
    Overrides:
    
    finalize in class AlgorithmBase
  - getWaveletImage
```
public ModelImage getWaveletImage()
```
    Accessor that returns the image.
    
    Returns:
    
    the wavelet image
  - runAlgorithm
```
public void runAlgorithm()
```
    Starts the program.
    
    Specified by:
    
    runAlgorithm in class AlgorithmBase
  - daub4
```
private void daub4(float[] a,
                   int n)
```
    DOCUMENT ME!
    
    Parameters:
    
    a - data vector to which Daubechies 4-coefficient wavelet filter or its transpose (for transformDir == INVERSE) is applied
    
    n - DOCUMENT ME!
  - pwt
```
private void pwt(float[] a,
                 int n)
```
    DOCUMENT ME!
    
    Parameters:
    
    a - data to which wavelet filter (for transformDir == FORWARD) or to which transpose wavelet filter is applied (for transformDir == INVERSE)
    
    n - Used hierarchically by routines wt1 and wtn
  - wt1
```
private void wt1(float[] a)
```
    DOCUMENT ME!
    
    Parameters:
    
    a - data replaced by its wavelet transform for transformDir == FORWARD or by its inverse wavelet transform for transformDir == INVERSE One dimensional discrete wavelet transform. Note that the length of a must be an integer power of 2
  - wtn
```
private void wtn(float[] a)
```
    DOCUMENT ME!
    
    Parameters:
    
    a - data replaced by its wavelet transform for transformDir == FORWARD or by its inverse wavelet transform for transformDir == INVERSE n-dimensional discrete wavelet transform. Note that the length of each dimension of a must be an integer power of 2

Class AlgorithmWaveletThreshold

Nested Class Summary

Nested classes/interfaces inherited from class java.lang.Thread

Field Summary

Fields inherited from class gov.nih.mipav.model.algorithms.AlgorithmBase

Fields inherited from class java.lang.Thread

Constructor Summary

Method Summary

Methods inherited from class gov.nih.mipav.model.algorithms.AlgorithmBase

Methods inherited from class java.lang.Thread

Methods inherited from class java.lang.Object

Field Detail

INVERSE

FORWARD

DAUB4

PWT

C0

C1

C2

C3

c4

c12

c20

HARD

SOFT

NONNEGATIVE_GARROTE

SCAD

aArray

aCutoff

aExp

aLog

aMax

arrayLength

belowThreshold

cc

cm2

cNum

cr

dataType

doWaveletImage

extents

filterType

foundSize

ioff

joff

minSize

nDims

newArrayLength

newExtents

newXDim

newYDim

newZDim

offsetX

offsetY

offsetZ

threshold

thresholdType

transformDir

waveletImage

xDim

yDim

zDim

xy

newXY

Constructor Detail

AlgorithmWaveletThreshold

AlgorithmWaveletThreshold

Method Detail

finalize

getWaveletImage

runAlgorithm

daub4

pwt

wt1

wtn