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Cell[CellGroupData[{
Cell["Haar Transform 2D", "Title"],

Cell["\<\
Wavelet Workshop
June 4-7, 2008
University of St. Thomas\
\>", "Subtitle",
 CellChangeTimes->{{3.421426484890625*^9, 3.42142648821875*^9}}],

Cell["\<\
Catherine Beneteau
Caroline Haddad
David Ruch
Patrick Van Fleet\
\>", "Subsubtitle",
 CellChangeTimes->{{3.42144927371875*^9, 3.42144928703125*^9}}],

Cell[CellGroupData[{

Cell["Objective", "Section"],

Cell["\<\
In this notebook, we will explore the two-dimensional discrete Haar wavelet \
transform.\
\>", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Conventions", "Section"],

Cell[TextData[{
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 StyleBox["DiscreteWavelets",
  FontColor->RGBColor[1, 0, 0]],
 " (written by Patrick Van Fleet).  All commands from the ",
 StyleBox["DiscreteWavelets",
  FontColor->RGBColor[1, 0, 0]],
 " library will be denoted in ",
 StyleBox["red",
  FontColor->RGBColor[1, 0, 0]],
 ".  Help is available for every command in ",
 StyleBox["the package",
  FontColor->GrayLevel[0]],
 ".  Click on Help and then Documentation Center.  At the bottom-right of the \
page is a link for Installed AddOns.  Click this link and one of the options \
is DiscreteWavelets.  Click this link to go to the Help Browser.  Like all ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " help screens, the help is \"live\" - you can either execute the commands \
in the help to see the effects of the command or cut and paste them into your \
own notebook.\n\nComments are useful within cells of code.  Any code enclosed \
by (*  *) is a comment and ignored by the ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " kernel."
}], "Text",
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}, Open  ]],

Cell[CellGroupData[{

Cell["Load DiscreteWavelets", "Section",
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Cell[BoxData[
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Cell[CellGroupData[{

Cell["Two-Dimensional Discrete Haar Transform Modules", "Section"],

Cell[TextData[{
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 StyleBox["DiscreteWavelets",
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 " and ",
 StyleBox["IHWT2D",
  FontColor->RGBColor[1, 0, 0]],
 ".  Both modules require two arguments.  The first is the input matrix.  The \
second argument is the number of iterations."
}], "Text",
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Cell[CellGroupData[{

Cell["Available Images", "Section",
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Cell[TextData[{
 "The ",
 StyleBox["DiscreteWavelets",
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 " packages comes with 18 grayscale images.  You can see information about \
these images (name, size, etc.) by issuing the command ",
 StyleBox["ImageList",
  FontColor->RGBColor[1, 0, 0]],
 "."
}], "Text",
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Cell[TextData[{
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 StyleBox["ShowThumbnails",
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 ".  "
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Cell[TextData[{
 "No matter where you installed the ",
 StyleBox["DiscreteWavelets",
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 " package on your computer, you can retrieve the absolute path and file name \
for each included image.  The command ",
 StyleBox["ImageNames",
  FontColor->RGBColor[1, 0, 0]],
 " produces a list of file names."
}], "Text",
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Cell["Loading and Plotting Images", "Section",
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Cell["\<\
Once you have the list of file names, it is very easy to load and plot \
images.  Let's load the first image in the list.\
\>", "Text",
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Cell["Using HWT2D", "Section",
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Cell["\<\
In the cell below, we compute and plot the two-dimensional HWT of image A.  \
We compute the transform of N[A] to speed up the computation.\
\>", "Text",
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Cell[CellGroupData[{

Cell["Using IHWT2D", "Section",
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Cell["\<\
In the cell below, we compute the inverse transform of the image.\
\>", "Text"],

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Cell[CellGroupData[{

Cell["Iterating the Process", "Section"],

Cell[TextData[{
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HWT.  In this case, the ",
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 StyleBox["Warning: ",
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 " Make sure to know the maximum amount of iterations you can compute before \
proceeding!!  You can use ImageList to display the maximum number of \
iterations that can be performed on each of the included images."
}], "Text",
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Cell["\<\
Here we compute four iterations of the Haar wavelet transformation.\
\>", "Text",
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Cell["\<\
You can plot various portions of the transform.  Here is the vertical portion \
of the third iteration.\
\>", "Text",
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