This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# WaveletMapIndexed

 WaveletMapIndexedapplies the function f to the arrays of coefficients and indices of a ContinuousWaveletData or DiscreteWaveletData object. WaveletMapIndexedapplies f to the DiscreteWaveletData coefficients specified by wind. WaveletMapIndexedapplies f to the ContinuousWaveletData coefficients specified by octvoc.
• Each should return an array or Image of the same dimensions as .
• For Sound and SampledSoundList, each is given as a list of vectors, each corresponding to a channel of sound samples.
Rescale all coefficients of a discrete wavelet transform by 20:
Normal gives the array of coefficients:
Compare with the unmodified coefficients:
Amplify the coefficient of the stationary wavelet transform of an image:
The inverse wavelet transform gives an image with vertical edges sharpened:
Rescale all coefficients of a discrete wavelet transform by 20:
 Out[2]=
Normal gives the array of coefficients:
 Out[3]=
Compare with the unmodified coefficients:
 Out[4]=

Amplify the coefficient of the stationary wavelet transform of an image:
 Out[1]=
 Out[2]=
The inverse wavelet transform gives an image with vertical edges sharpened:
 Out[3]=
 Scope   (11)
Apply an arbitrary function to all coefficients of a discrete wavelet transform:
Apply a symbolic function that also depends on the wavelet index for each coefficient vector:
The result is a wavelet data object of the same type:
The modified data can be used in other wavelet functions such as inverse wavelet transforms:
Transform only specified coefficients in DiscreteWaveletData:
Apply a function to detail coefficients only, using the index pattern :
Apply a function to coarse coefficients only, using the index pattern :
Transform only specified coefficients in a ContinuousWaveletData:
Apply a function to coefficients in the first octave only:
Apply a function to all coefficients except those in the second octave, first voice :
The function f can depend on the wavelet index as its second argument:
Define a function with an arbitrary dependence on the wavelet index:
Apply the function to continuous wavelet transform coefficients:
For list data, the coefficients supplied as the first argument of f are lists:
Apply a function that transforms lists:
For multidimensional data, the coefficients are arrays of the same depth:
Apply a function that transforms array coefficients of that depth:
For image data, the coefficients are supplied to f as Image objects:
The coefficients have the same number of channels as the original image:
Apply a function that transforms image coefficients:
For sound data, the coefficients are two-dimensional arrays:
Dimensions of one coefficient:
The two dimensions specify the channel number and the wavelet coefficients for that channel:
Apply a function that transforms two-channel data:
Reconstructed Sound data:
 Applications   (7)
Coefficients with short indices correspond to small-scale structure in the data:
Zero all small-scale coefficients from the stationary wavelet transform of random data:
The inverse wavelet transform varies only on larger scales:
Perform a simple thresholding operation by removing low-amplitude wavelet coefficients:
Compare with the original data:
Blur an image by setting small-scale detail coefficients to zero:
Compare with the original image:
Sharpen an image by amplifying small-scale detail coefficients:
Compare with the original image:
Use a mask image to vary between blurring and sharpening across an image:
Compare with the original image:
Apply a nonlinear function to wavelet coefficients for sound data:
Inverse transform to obtain a reconstructed sound object:
Perform a wavelet-based shrinkage based on conditional mean:
Compute a discrete wavelet transform up to refinement level 6:
Compute the standard deviation for the finest detail coefficients:
Compute the standard deviation for all wavelet coefficients:
Assuming a Gaussian mixture model, variance can be estimated in the proportion to :
Shrinkage estimates of the signal coefficients are given by:
Use WaveletMapIndexed to map over detail coefficients:
Reconstruct thresholded signal coefficients:
MapIndexed applies f to the parts of any expression:
WaveletMapIndexed applies f to the coefficients in the wavelet data object wd:
WaveletMapIndexed applies f to each part of each coefficient:
MapIndexed gives the part specification as the second argument of f:
WaveletMapIndexed gives the wavelet index specification as the second argument of f:
WaveletMapIndexed transforms arrays of coefficients, giving a new DiscreteWaveletData:
Use Map and Normal[dwd] to transform coefficients into normal expressions:
Or use ReplaceAll ():
The function f is always passed the index specification as its second argument:
Use a function that operates on its first argument only:
The function f should return an array or image of the same dimensions:
Listable functions return an array of the same dimensions:
Arithmetic operations such as multiplication are Listable:
Use Map for functions that are not Listable:
New in 8