c09ezf inserts a selected set of two-dimensional discrete wavelet transform (DWT) coefficients into the full set of coefficients stored in compact form, which may be later used as input to the multi-level reconstruction routine
c09edf.
c09ezf inserts a selected set of two-dimensional DWT coefficients into the full set of coefficients stored in compact form in a one-dimensional array
c. It is required that
c09ezf is preceded by a call to the initialization routine
c09abf and the forward multi-level transform routine
c09ecf.
Given an initial two-dimensional data set
$A$, a prior call to
c09ecf computes the approximation coefficients (at the highest requested level) and three sets of detail coefficients at all levels and stores these in compact form in a one-dimensional array
c.
c09eyf can then extract either the approximation coefficients or one of the sets of detail coefficients at one of the levels
into a two-dimensional array,
d. Following some calculation on this set of coefficients (for example, denoising), the updated coefficients in
d are inserted back into the full set
c using
c09ezf. Several extractions and insertions may be performed at different levels.
c09edf can then be used to reconstruct a manipulated data set
$\stackrel{~}{A}$. The dimensions of
d depend on the level extracted and are available from the arrays
dwtlvm and
dwtlvn as returned by
c09ecf which contain the first and second dimensions respectively. See
Section 2.1 in the
C09 Chapter Introduction for a discussion of the multi-level two-dimensional DWT.
None.
Note: the following notation is used in this section:
- ${n}_{\mathrm{cm}}$ is the number of wavelet coefficients in the first dimension, which, at level ilev, is equal to ${\mathbf{dwtlvm}}\left({\mathbf{nwl}}-{\mathbf{ilev}}+1\right)$ as returned by a call to c09ecf transforming nwl levels.
- ${n}_{\mathrm{cn}}$ is the number of wavelet coefficients in the second dimension, which, at level ilev, is equal to ${\mathbf{dwtlvn}}\left({\mathbf{nwl}}-{\mathbf{ilev}}+1\right)$ as returned by a call to c09ecf transforming nwl levels
If on entry
${\mathbf{ifail}}=0$ or
$-1$, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
Not applicable.
None.
The following example demonstrates using the coefficient extraction and insertion routines in order to apply denoising using a thresholding operation. The original input data, which is horizontally striped, has artificial noise introduced to it, taken from a normal random number distribution. Reconstruction then takes place on both the noisy data and denoised data. The Mean Square Errors (MSE) of the two reconstructions are printed along with the reconstruction of the denoised data. The MSE of the denoised reconstruction is less than that of the noisy reconstruction.