WaveletImagePlot
plots the basis tree of wavelet image coefficients in the DiscreteWaveletData dwd.
applies the image function ifunc to coefficients and wavelet indexes before plotting.
Details and Options


- WaveletImagePlot assembles a single image using a pyramid of images.
- WaveletImagePlot arranges coefficients in the same way as WaveletMatrixPlot.
- WaveletImagePlot[dwd] is equivalent to WaveletImagePlot[dwd,Automatic], corresponding to the basis of coefficients used in the InverseWaveletTransform.
- The wavelet indices used in the Automatic setting are given by dwd["BasisIndex"].
- The dwd should be generated from image data and produced by DiscreteWaveletTransform, DiscreteWaveletPacketTransform, or LiftingWaveletTransform.
- WaveletImagePlot[dwd,r] plots basis coefficient images up to refinement level r when dwd comes from DiscreteWaveletTransform or LiftingWaveletTransform.
- WaveletImagePlot[dwd,r] plots all coefficient images at refinement level r when dwd comes from DiscreteWaveletPacketTransform.
- In WaveletImagePlot[dwd,r,ifunc], each ifunc[coefi,windi] should yield an Image with the same dimensions as coefi.
- WaveletImagePlot has the same options as Image, with the following additions and changes: [List of all options]
-
BaseStyle Black what base color to use between images PlotLayout Automatic what layout to use for the plot - Possible settings for PlotLayout include: "Pyramid" and "Grid".
- BaseStyle is used to specify the color of pixels to use at coefficient boundaries.
- With the setting Method->"InverseTransform", the inverse transform of each coefficient array will be plotted.
- WaveletImagePlot returns an Image object.
-
AlignmentPoint Center the default point in the graphic to align with BaselinePosition Automatic how to align with a surrounding text baseline BaseStyle Black what base color to use between images ColorSpace Automatic what color space to assume for the data ImageResolution Automatic the resolution when displayed or exported ImageSize Automatic display size of the image Interleaving Automatic whether to assume channels are interleaved Magnification Automatic how to magnify the displayed image MetaInformation < > metainformation associated with the image PlotLayout Automatic what layout to use for the plot
List of all options

Examples
open allclose allBasic Examples (2)Summary of the most common use cases
Show wavelet image coefficients arranged in a pyramid layout:

https://wolfram.com/xid/0bc63yl430efxlu-bz8777

https://wolfram.com/xid/0bc63yl430efxlu-jdvncb

Plot wavelet image coefficients in a grid layout:

https://wolfram.com/xid/0bc63yl430efxlu-yatdxw

Plot a full tree of wavelet packet coefficients at different refinement levels:

https://wolfram.com/xid/0bc63yl430efxlu-mw5of9

https://wolfram.com/xid/0bc63yl430efxlu-gtaeae

Scope (9)Survey of the scope of standard use cases
Data (5)
DiscreteWaveletTransform of image data:

https://wolfram.com/xid/0bc63yl430efxlu-mha6d

Plot image wavelet coefficients in a hierarchical grid:

https://wolfram.com/xid/0bc63yl430efxlu-izx63

The plotted coefficients are the Automatic coefficients used in the inverse transform:

https://wolfram.com/xid/0bc63yl430efxlu-ni8wjg

Use WaveletImagePlot[dwd,r] to plot coefficients only up to refinement level r:

https://wolfram.com/xid/0bc63yl430efxlu-f9436u

https://wolfram.com/xid/0bc63yl430efxlu-ela2wh

The hierarchical layout corresponds to the tree structure of the wavelet coefficients:

https://wolfram.com/xid/0bc63yl430efxlu-dzbl1g

DiscreteWaveletPacketTransform of image data:

https://wolfram.com/xid/0bc63yl430efxlu-f5wt0m

The DiscreteWaveletData object contains a full tree of coefficients at each level:

https://wolfram.com/xid/0bc63yl430efxlu-bo2ekx

Default Automatic coefficients for packet transform correspond to the highest refinement level:

https://wolfram.com/xid/0bc63yl430efxlu-dr6xa5

https://wolfram.com/xid/0bc63yl430efxlu-xw74k

WaveletBestBasis computes a different Automatic tree of coefficients:

https://wolfram.com/xid/0bc63yl430efxlu-giw325

Specify an image function f to apply to wavelet coefficients before plotting:

https://wolfram.com/xid/0bc63yl430efxlu-05mf8

https://wolfram.com/xid/0bc63yl430efxlu-dw5yx5

By default, ImageAdjust[ImageApply[Abs,#]& is applied:

https://wolfram.com/xid/0bc63yl430efxlu-blm7l7

Presentation (4)

https://wolfram.com/xid/0bc63yl430efxlu-iodd3o

https://wolfram.com/xid/0bc63yl430efxlu-lxd3n

Specify a function to apply to each coefficient image:

https://wolfram.com/xid/0bc63yl430efxlu-f5de31

https://wolfram.com/xid/0bc63yl430efxlu-cdgg9j


https://wolfram.com/xid/0bc63yl430efxlu-wjzutv

Control the displayed size of the generated image:

https://wolfram.com/xid/0bc63yl430efxlu-em1on6

https://wolfram.com/xid/0bc63yl430efxlu-ez6p1z

Specify a style for grid lines separating wavelet coefficients:

https://wolfram.com/xid/0bc63yl430efxlu-k0se0s

https://wolfram.com/xid/0bc63yl430efxlu-ftb0oz

Options (4)Common values & functionality for each option
BaseStyle (1)
ImageSize (1)
Specify the size of the displayed image:

https://wolfram.com/xid/0bc63yl430efxlu-b20038

https://wolfram.com/xid/0bc63yl430efxlu-gt72lv

The pixel dimensions of the image are not affected by ImageSize:

https://wolfram.com/xid/0bc63yl430efxlu-ckj1lh

Method (2)
Inverse transform each coefficient before plotting:

https://wolfram.com/xid/0bc63yl430efxlu-ueir5v
Inverse transform coefficients from stationary wavelet transform:

https://wolfram.com/xid/0bc63yl430efxlu-cv9b4p

https://wolfram.com/xid/0bc63yl430efxlu-d2854h

Inverse transform coefficients from lifting wavelet transform:

https://wolfram.com/xid/0bc63yl430efxlu-zngtwx

https://wolfram.com/xid/0bc63yl430efxlu-buy5yn

Choose which channel to plot in multichannel Image:

https://wolfram.com/xid/0bc63yl430efxlu-dhxajp

https://wolfram.com/xid/0bc63yl430efxlu-477q0o

Properties & Relations (6)Properties of the function, and connections to other functions
WaveletImagePlot returns an Image object:

https://wolfram.com/xid/0bc63yl430efxlu-gbvpwp

https://wolfram.com/xid/0bc63yl430efxlu-gp8n7l


https://wolfram.com/xid/0bc63yl430efxlu-br1svm

Pixel dimensions of generated images depend on padding, wavelet, and refinement level:

https://wolfram.com/xid/0bc63yl430efxlu-d9abgo

https://wolfram.com/xid/0bc63yl430efxlu-expxfd

The generated image is generally larger than the original data:

https://wolfram.com/xid/0bc63yl430efxlu-2m5co

WaveletImagePlot plots image wavelet coefficients in a hierarchical grid layout:

https://wolfram.com/xid/0bc63yl430efxlu-nys1d0

https://wolfram.com/xid/0bc63yl430efxlu-cb34xq

dwd[…,"Image"] gives each coefficient as a separate image:

https://wolfram.com/xid/0bc63yl430efxlu-iylho

WaveletImagePlot plots the Automatic coefficients used in the inverse transform:

https://wolfram.com/xid/0bc63yl430efxlu-bhauuw

https://wolfram.com/xid/0bc63yl430efxlu-k8adhz

WaveletBestBasis selects a different default tree of coefficients:

https://wolfram.com/xid/0bc63yl430efxlu-ndabl8

https://wolfram.com/xid/0bc63yl430efxlu-k5jepu

WaveletMatrixPlot plots matrix wavelet coefficients in a hierarchical grid:

https://wolfram.com/xid/0bc63yl430efxlu-dd59u4

https://wolfram.com/xid/0bc63yl430efxlu-bgp78f

https://wolfram.com/xid/0bc63yl430efxlu-eb14aw

WaveletScalogram plots vector coefficients with numerical magnitude indicated by color:

https://wolfram.com/xid/0bc63yl430efxlu-i7b594

https://wolfram.com/xid/0bc63yl430efxlu-e10aos

https://wolfram.com/xid/0bc63yl430efxlu-nbuq3

WaveletListPlot plots vector coefficients with a common horizontal or vertical axis:

https://wolfram.com/xid/0bc63yl430efxlu-be79uu

Possible Issues (3)Common pitfalls and unexpected behavior
Generated images may be saturated if a custom image function f is specified:

https://wolfram.com/xid/0bc63yl430efxlu-k1rk7

https://wolfram.com/xid/0bc63yl430efxlu-bvpk7a

Compose the custom image function with ImageAdjust:

https://wolfram.com/xid/0bc63yl430efxlu-p1x5k

Wavelet coefficients from stationary wavelet transform cannot be plotted using pyramid layout:

https://wolfram.com/xid/0bc63yl430efxlu-0w6ql6


https://wolfram.com/xid/0bc63yl430efxlu-ovvjtn


Pyramid layout cannot be constructed for inverse transformed wavelet coefficients:

https://wolfram.com/xid/0bc63yl430efxlu-vzlsr7


https://wolfram.com/xid/0bc63yl430efxlu-n92fs


Neat Examples (2)Surprising or curious use cases

https://wolfram.com/xid/0bc63yl430efxlu-5pu5q3
Improve contrast for detail coefficients:

https://wolfram.com/xid/0bc63yl430efxlu-8fgn9t

https://wolfram.com/xid/0bc63yl430efxlu-5xea8w

Plot an image wavelet packet transform:

https://wolfram.com/xid/0bc63yl430efxlu-mtur5u


https://wolfram.com/xid/0bc63yl430efxlu-p1e7m

https://wolfram.com/xid/0bc63yl430efxlu-de9b1d

Wolfram Research (2010), WaveletImagePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletImagePlot.html.
Text
Wolfram Research (2010), WaveletImagePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletImagePlot.html.
Wolfram Research (2010), WaveletImagePlot, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletImagePlot.html.
CMS
Wolfram Language. 2010. "WaveletImagePlot." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WaveletImagePlot.html.
Wolfram Language. 2010. "WaveletImagePlot." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WaveletImagePlot.html.
APA
Wolfram Language. (2010). WaveletImagePlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WaveletImagePlot.html
Wolfram Language. (2010). WaveletImagePlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WaveletImagePlot.html
BibTeX
@misc{reference.wolfram_2025_waveletimageplot, author="Wolfram Research", title="{WaveletImagePlot}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/WaveletImagePlot.html}", note=[Accessed: 08-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_waveletimageplot, organization={Wolfram Research}, title={WaveletImagePlot}, year={2010}, url={https://reference.wolfram.com/language/ref/WaveletImagePlot.html}, note=[Accessed: 08-July-2025
]}