naginterfaces.library.wav.dim3_​mxolap_​multi_​inv

naginterfaces.library.wav.dim3_mxolap_multi_inv(nwlinv, c, m, n, fr, comm)

dim3_mxolap_multi_inv computes the inverse three-dimensional multi-level discrete wavelet transform (IDWT). This function reconstructs data from (possibly filtered or otherwise manipulated) wavelet transform coefficients calculated by dim3_multi_fwd() from an original input array. The initialization function dim3_init() must be called first to set up the IDWT options.

For full information please refer to the NAG Library document for c09fd

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/c09/c09fdf.html

Parameters

nwlinvint

The number of levels to be used in the inverse multi-level transform. The number of levels must be less than or equal to $n_{fwd}$, which has the value of argument $\text{nwl}$ as used in the computation of the wavelet coefficients using dim3_multi_fwd(). The data will be reconstructed to level $(\text{nwl}-nwlinv)$, where level $0$ is the original input dataset provided to dim3_multi_fwd().

cfloat, array-like, shape $\left(\text{lenc}\right)$

The coefficients of the multi-level discrete wavelet transform. This will normally be the result of some transformation on the coefficients computed by function dim3_multi_fwd().

Note that the coefficients in $c$ may be extracted according to level and type into three-dimensional arrays using dim3_coeff_ext(), and inserted using dim3_coeff_ins().

mint

The number of elements, $m$, in the first dimension of the reconstructed array $B$. For a full reconstruction of $\text{nwl}$ levels, where $\text{nwl}$ is as supplied to dim3_multi_fwd(), this must be the same as argument $\text{m}$ used in a preceding call to dim3_multi_fwd(). For a partial reconstruction of $nwlinv<\text{nwl}$ levels, this must be equal to $\text{dwtlvm}\left[nwlinv\right]$, as returned from dim3_multi_fwd()

nint

The number of elements, $n$, in the second dimension of the reconstructed array $B$. For a full reconstruction of $\text{nwl}$, levels, where $\text{nwl}$ is as supplied to dim3_multi_fwd(), this must be the same as argument $\text{n}$ used in a preceding call to dim3_multi_fwd(). For a partial reconstruction of $nwlinv<\text{nwl}$ levels, this must be equal to $\text{dwtlvn}\left[nwlinv\right]$, as returned from dim3_multi_fwd().

frint

The number of elements, $\text{fr}$, in the third dimension of the reconstructed array $B$. For a full reconstruction of $\text{nwl}$ levels, where $\text{nwl}$ is as supplied to dim3_multi_fwd(), this must be the same as argument $fr$ used in a preceding call to dim3_multi_fwd(). For a partial reconstruction of $nwlinv<\text{nwl}$ levels, this must be equal to $\text{dwtlvfr}\left[nwlinv\right]$, as returned from dim3_multi_fwd().

commdict, communication object

Communication structure.

This argument must have been initialized by a prior call to dim3_init().

Returns

bfloat, ndarray, shape $(m,n,fr)$

The $m\times n\times \text{fr}$ reconstructed array, $B$, with $B_{ijk}$ stored in $b[i-1,j-1,k-1]$. The reconstruction is based on the input multi-level wavelet transform coefficients and the transform options supplied to the initialization function dim3_init().

Raises

NagValueError

(errno $1$)

On entry, $nwlinv=⟨value⟩$ and $\text{nwl}=⟨value⟩$ where $\text{nwl}$ is as used in the computation of the wavelet coefficients by a call to dim3_multi_fwd().

Constraint: $nwlinv\le \text{nwl}$ as used in the call to dim3_multi_fwd().

(errno $1$)

On entry, $nwlinv=⟨value⟩$.

Constraint: $nwlinv\ge 1$.

(errno $3$)

On entry, $\text{lenc}=⟨value⟩$.

Constraint: $\text{lenc}\ge ⟨value⟩$, the number of wavelet coefficients required for a transform operating on $nwlinv$ levels. If $nwlinv=\text{nwlmax}$, the maximum number of levels as returned by the initial call to dim3_init(), $\text{lenc}$ must be at least $n_{ct}$, the value returned in $\text{nwct}$ by the same call to dim3_init().

(errno $4$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge ⟨value⟩$, the number of coefficients in the second dimension at the required level of reconstruction.

(errno $4$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge ⟨value⟩$, the number of coefficients in the first dimension at the required level of reconstruction.

(errno $4$)

On entry, $fr=⟨value⟩$.

Constraint: $fr\ge ⟨value⟩$, the number of coefficients in the third dimension at the required level of reconstruction.

(errno $6$)

Either the communication array $comm$[‘icomm’] has been corrupted or there has not been a prior call to the initialization function dim3_init().

(errno $6$)

Either the initialization function was called with $wtrans=\text{‘S'}$ or the communication array $comm$[‘icomm’] has been corrupted.

Notes

dim3_mxolap_multi_inv performs the inverse operation of dim3_multi_fwd(). That is, given a set of wavelet coefficients, computed up to level $n_{fwd}$ by dim3_multi_fwd() using a DWT as set up by the initialization function dim3_init(), on a real three-dimensional array, $A$, dim3_mxolap_multi_inv 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 dim3_multi_fwd(). This results in a partial reconstruction.

References

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)