Three-dimensional discrete wavelet transforms (DWT) are characterised by the mother wavelet, the end extension method and whether multiresolution analysis is to be performed. For the selected combination of choices for these three characteristics, and for given dimensions (
) of data array
,
nag_wfilt_3d (c09acc) returns the dimension details for the transform determined by this combination. The dimension details are:
, the maximum number of levels of resolution that would be computed were a multi-level DWT applied;
, the filter length;
the total number of wavelet coefficients (over all levels in the multi-level DWT case);
, the number of coefficients in the second dimension for a single-level DWT; and
, the number of coefficients in the third dimension for a single-level DWT. These values are also stored in the communication array
icomm, as are the input choices, so that they may be conveniently communicated to the three-dimensional transform functions in this chapter.
None.
- 1:
– Nag_WaveletInput
-
On entry: the name of the mother wavelet. See the
c09 Chapter Introduction for details.
- Haar wavelet.
- , where
- Daubechies wavelet with vanishing moments ( coefficients). For example, is the name for the Daubechies wavelet with vanishing moments ( coefficients).
- , where can be one of 1_1, 1_3, 1_5, 2_2, 2_4, 2_6, 2_8, 3_1, 3_3, 3_5 or 3_7
- Biorthogonal wavelet of order .. For example is the name for the Biorthogonal wavelet of order .
Constraint:
, , , , , , , , , , , , , , , , , , , or .
- 2:
– Nag_WaveletTransformInput
-
On entry: the type of discrete wavelet transform that is to be applied.
- Single-level decomposition or reconstruction by discrete wavelet transform.
- Multiresolution, by a multi-level DWT or its inverse.
Constraint:
or .
- 3:
– Nag_WaveletModeInput
-
On entry: the end extension method.
- Periodic end extension.
- Half-point symmetric end extension.
- Whole-point symmetric end extension.
- Zero end extension.
Constraint:
, , or .
- 4:
– IntegerInput
-
On entry: the number of elements, , in the first dimension (number of rows of each two-dimensional frame) of the input data, .
Constraint:
.
- 5:
– IntegerInput
-
On entry: the number of elements, , in the second dimension (number of columns of each two-dimensional frame) of the input data, .
Constraint:
.
- 6:
– IntegerInput
-
On entry: the number of elements, , in the third dimension (number of frames) of the input data, .
Constraint:
.
- 7:
– Integer *Output
-
On exit: the maximum number of levels of resolution,
, that can be computed if a multi-level discrete wavelet transform is applied (
). It is such that
, for
an integer.
If
,
nwlmax is not set.
- 8:
– Integer *Output
-
On exit: the filter length, , for the supplied mother wavelet. This is used to determine the number of coefficients to be generated by the chosen transform.
- 9:
– Integer *Output
-
On exit: the total number of wavelet coefficients, , that will be generated. When the number of rows required (i.e., the first dimension of each two-dimensional frame) in each of the output coefficient arrays can be calculated as . When the length of the array used to store all of the coefficient matrices must be at least .
- 10:
– Integer *Output
-
On exit: for a single-level transform (), the number of coefficients that would be generated in the second dimension, , for each coefficient type. For a multi-level transform () this is set to .
- 11:
– Integer *Output
-
On exit: for a single-level transform (), the number of coefficients that would be generated in the third dimension, , for each coefficient type. For a multi-level transform () this is set to .
- 12:
– IntegerCommunication Array
-
On exit: contains details of the wavelet transform and the problem dimension which is to be communicated to the two-dimensional discrete transform functions in this chapter.
- 13:
– NagError *Input/Output
-
The NAG error argument (see
Section 3.7 in How to Use the NAG Library and its Documentation).
Not applicable.
None.