c09fyc extracts a selected set of discrete wavelet transform (DWT) coefficients from the full set of coefficients stored in compact form, as computed by
c09fac (single level three-dimensional DWT) or
c09fcc (multi-level three-dimensional DWT).
c09fyc is intended to be used after a call to either
c09fac (single level three-dimensional DWT) or
c09fcc (multi-level three-dimensional DWT), either of which must be preceded by a call to
c09acc (three-dimensional wavelet filter initialization). Given an initial three-dimensional data set
$A$, a prior call to
c09fac or
c09fcc computes the approximation coefficients (at the highest requested level in the case of
c09fcc) and seven sets of detail coefficients (at all levels in the case of
c09fcc) and stores these in compact form in a one-dimensional array
c.
c09fyc can then extract either the approximation coefficients or one of the sets of detail coefficients (at one of the levels following
c09fcc) into a three-dimensional data set stored in
d.
If a multi-level DWT was performed by a prior call to
c09fcc then the dimensions of the three-dimensional data stored in
d depend on the level extracted and are available from the arrays
dwtlvm,
dwtlvn and
dwtlvfr as returned by
c09fcc which contain the first, second and third dimensions respectively.
If a single level DWT was performed by a prior call to
c09fac then the dimensions of the three-dimensional data stored in
d can be determined from
nwct,
nwcn and
nwcfr as returned by the setup function
c09acc.
See
Section 2.1 in the
C09 Chapter Introduction for a discussion of the three-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. Following a call to c09fac (i.e., when ${\mathbf{ilev}}=0$) this is equal to ${\mathbf{nwct}}/(8\times {\mathbf{nwcn}}\times {\mathbf{nwcfr}})$ as returned by c09acc. Following a call to c09fcc transforming nwl levels, and when extracting at level ${\mathbf{ilev}}>0$, this is equal to ${\mathbf{dwtlvm}}\left[{\mathbf{nwl}}-{\mathbf{ilev}}\right]$.
- ${n}_{\mathrm{cn}}$ is the number of wavelet coefficients in the second dimension. Following a call to c09fac (i.e., when ${\mathbf{ilev}}=0$) this is equal to nwcn as returned by c09acc. Following a call to c09fcc transforming nwl levels, and when extracting at level ${\mathbf{ilev}}>0$, this is equal to ${\mathbf{dwtlvn}}\left[{\mathbf{nwl}}-{\mathbf{ilev}}\right]$.
- ${n}_{\mathrm{cfr}}$ is the number of wavelet coefficients in the third dimension. Following a call to c09fac (i.e., when ${\mathbf{ilev}}=0$) this is equal to nwcfr as returned by c09acc. Following a call to c09fcc transforming nwl levels, and when extracting at level ${\mathbf{ilev}}>0$, this is equal to ${\mathbf{dwtlvfr}}\left[{\mathbf{nwl}}-{\mathbf{ilev}}\right]$
Not applicable.
None.