NAG CL Interface
c09ezc (dim2_​coeff_​ins)

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1 Purpose

c09ezc 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 function c09edc.

2 Specification

#include <nag.h>
void  c09ezc (Integer ilev, Integer cindex, Integer lenc, double c[], const double d[], Integer pdd, Integer icomm[], NagError *fail)
The function may be called by the names: c09ezc, nag_wav_dim2_coeff_ins or nag_wav_2d_coeff_ins.

3 Description

c09ezc 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 c09ezc is preceded by a call to the initialization function c09abc and the forward multi-level transform function c09ecc.
Given an initial two-dimensional data set A, a prior call to c09ecc 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. c09eyc can then extract either the approximation coefficients or one of the sets of detail coefficients at one of the levels as two-dimensional data into the 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 c09ezc. Several extractions and insertions may be performed at different levels. c09edc can then be used to reconstruct a manipulated data set A~. The dimensions of the two-dimensional data stored in d depend on the level extracted and are available from the arrays dwtlvm and dwtlvn as returned by c09ecc 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.

4 References

None.

5 Arguments

Note: the following notation is used in this section:
1: ilev Integer Input
On entry: the level at which coefficients are to be inserted.
Constraints:
  • 1ilevnwl, where nwl is as used in a preceding call to c09ecc;
  • if cindex=0, ilev=nwl.
2: cindex Integer Input
On entry: identifies which coefficients to insert. The coefficients are identified as follows:
cindex=0
The approximation coefficients, produced by application of the low pass filter over columns and rows of the original matrix (LL). The approximation coefficients are present only for ilev=nwl, where nwl is the value used in a preceding call to c09ecc.
cindex=1
The vertical detail coefficients produced by applying the low pass filter over columns of the original matrix and the high pass filter over rows (LH).
cindex=2
The horizontal detail coefficients produced by applying the high pass filter over columns of the original matrix and the low pass filter over rows (HL).
cindex=3
The diagonal detail coefficients produced by applying the high pass filter over columns and rows of the original matrix (HH).
Constraint: 0cindex3 when ilev=nwl as used in c09ecc, otherwise 1cindex3.
3: lenc Integer Input
On entry: the dimension of the array c.
Constraint: lenc must be unchanged from the value used in the preceding call to c09ecc.
4: c[lenc] double Input/Output
On entry: contains the DWT coefficients inserted by previous calls to c09ezc, or computed by a previous call to c09ecc.
On exit: contains the same DWT coefficients provided on entry except for those identified by ilev and cindex, which are updated with the values supplied in d, inserted into the correct locations as expected by the reconstruction function c09edc.
5: d[dim] const double Input
Note: the dimension, dim, of the array d must be at least pdd×ncn.
On entry: the coefficients to be inserted.
If ilev=nwl (as used in c09ecc) and cindex=0, the ncm × ncn manipulated approximation coefficients aij must be stored in d[(j-1)×pdd+i-1], for i=1,2,,ncm and i=1,2,,ncn.
Otherwise the ncm × ncn manipulated level ilev detail coefficients (of type specified by cindex) dij must be stored in d[(j-1)×pdd+i-1] , for i=1,2,,ncm and j=1,2,,ncn.
6: pdd Integer Input
On entry: the stride separating row elements in the two-dimensional data stored in the array d.
Constraint: pddncm.
7: icomm[180] Integer Communication Array
On entry: contains details of the discrete wavelet transform and the problem dimension as setup in the call to the initialization function c09abc.
8: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

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 value had an illegal value.
NE_INITIALIZATION
Either the initialization function has not been called first or icomm has been corrupted.
Either the initialization function was called with wtrans=Nag_SingleLevel or icomm has been corrupted.
NE_INT
On entry, cindex=value.
Constraint: cindex3.
On entry, cindex=value.
Constraint: cindex0.
On entry, ilev=value.
Constraint: ilev1.
NE_INT_2
On entry, ilev=value and nwl=value.
Constraint: ilevnwl, where nwl is the number of levels used in the call to c09ecc.
On entry, lenc=value and nct=value.
Constraint: lencnct, where nct is the number of DWT coefficients computed in a previous call to c09ecc.
On entry, pdd=value and ncm=value.
Constraint: pddncm, where ncm is the number of DWT coefficients in the first dimension at the selected level ilev.
NE_INT_3
On entry, ilev=value and nwl=value, but cindex=0.
Constraint: cindex>0 when ilev<nwl in the preceding call to c09ecc.
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.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
c09ezc is not threaded in any implementation.

9 Further Comments

None.

10 Example

The following example demonstrates using the coefficient extraction and insertion functions 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.

10.1 Program Text

Program Text (c09ezce.c)

10.2 Program Data

Program Data (c09ezce.d)

10.3 Program Results

Program Results (c09ezce.r)