c09fdc computes the inverse threedimensional multilevel discrete wavelet transform (IDWT). This function reconstructs data from (possibly filtered or otherwise manipulated) wavelet transform coefficients calculated by
c09fcc from an original input array. The initialization function
c09acc must be called first to set up the IDWT options.
c09fdc performs the inverse operation of
c09fcc. That is, given a set of wavelet coefficients, computed up to level
${n}_{\mathrm{fwd}}$ by
c09fcc using a DWT as set up by the initialization function
c09acc, on a real threedimensional array,
$A$,
c09fdc will reconstruct
$A$. The reconstructed array is referred to as
$B$ in the following since it will not be identical to
$A$ when the DWT coefficients have been filtered or otherwise manipulated prior to reconstruction. If the original input array is level
$0$, then it is possible to terminate reconstruction at a higher level by specifying fewer than the number of levels used in the call to
c09fcc. This results in a partial reconstruction.
Wang Y, Che X and Ma S (2012) Nonlinear filtering based on 3D wavelet transform for MRI denoising URASIP Journal on Advances in Signal Processing 2012:40
 NE_ALLOC_FAIL

Dynamic memory allocation failed.
See
Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
 NE_BAD_PARAM

On entry, argument $\u2329\mathit{\text{value}}\u232a$ had an illegal value.
 NE_INITIALIZATION

Either the communication array
icomm has been corrupted or there has not been a prior call to the initialization function
c09acc.
The initialization function was called with ${\mathbf{wtrans}}=\mathrm{Nag\_SingleLevel}$.
 NE_INT

On entry, ${\mathbf{fr}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{fr}}\ge \u2329\mathit{\text{value}}\u232a$, the number of coefficients in the third dimension at the required level of reconstruction.
On entry, ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{m}}\ge \u2329\mathit{\text{value}}\u232a$, the number of coefficients in the first dimension at the required level of reconstruction.
On entry, ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{n}}\ge \u2329\mathit{\text{value}}\u232a$, the number of coefficients in the second dimension at the required level of reconstruction.
On entry, ${\mathbf{nwlinv}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{nwlinv}}\ge 1$.
 NE_INT_2

On entry, ${\mathbf{ldb}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{m}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{ldb}}\ge {\mathbf{m}}$.
On entry,
${\mathbf{lenc}}=\u2329\mathit{\text{value}}\u232a$.
Constraint:
${\mathbf{lenc}}\ge \u2329\mathit{\text{value}}\u232a$, the number of wavelet coefficients required for a transform operating on
nwlinv levels. If
${\mathbf{nwlinv}}={\mathbf{nwlmax}}$, the maximum number of levels as returned by the initial call to
c09acc,
lenc must be at least
${n}_{\mathrm{ct}}$, the value returned in
nwct by the same call to
c09acc.
On entry,
${\mathbf{nwlinv}}=\u2329\mathit{\text{value}}\u232a$ and
${\mathbf{nwl}}=\u2329\mathit{\text{value}}\u232a$ where
nwl is as used in the computation of the wavelet coefficients by a call to
c09fcc.
Constraint:
${\mathbf{nwlinv}}\le {\mathbf{nwl}}$ as used in the call to
c09fcc.
On entry, ${\mathbf{sdb}}=\u2329\mathit{\text{value}}\u232a$ and ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{sdb}}\ge {\mathbf{n}}$.
 NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact
NAG for assistance.
See
Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
 NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library CL Interface for further information.
The accuracy of the wavelet transform depends only on the floatingpoint operations used in the convolution and downsampling and should thus be close to machine precision.
None.