# naginterfaces.library.wav.dim3_​multi_​fwd¶

naginterfaces.library.wav.dim3_multi_fwd(a, nwl, comm)[source]

dim3_multi_fwd computes the three-dimensional multi-level discrete wavelet transform (DWT). The initialization function dim3_init() must be called first to set up the DWT options.

For full information please refer to the NAG Library document for c09fc

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/c09/c09fcf.html

Parameters
afloat, array-like, shape

The three-dimensional input data , where with stored in .

nwlint

The number of levels, , in the multi-level resolution to be performed.

commdict, communication object, modified in place

Communication structure.

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

Returns
cfloat, ndarray, shape

The coefficients of the discrete wavelet transform. If you need to access or modify the approximation coefficients or any specific set of detail coefficients then the use of dim3_coeff_ext() or dim3_coeff_ins() is recommended. For completeness the following description provides details of precisely how the coefficients are stored in but this information should only be required in rare cases.

Let denote the number of coefficients of each type at level , for , such that .

Then, letting and , for , the coefficients are stored in as follows:

, for

Contains the level approximation coefficients, . Note that for computational efficiency reasons these coefficients are stored as in .

, for

Contains the level detail coefficients. These are:

LLH coefficients if ;

LHL coefficients if ;

LHH coefficients if ;

HLL coefficients if ;

HLH coefficients if ;

HHL coefficients if ;

HHH coefficients if ,

for . See the C09 Introduction for a description of how these coefficients are produced.

Note that for computational efficiency reasons these coefficients are stored as in .

dwtlvmint, ndarray, shape

The number of coefficients in the first dimension for each coefficient type at each level. contains the number of coefficients in the first dimension (for each coefficient type computed) at the ()th level of resolution, for .

dwtlvnint, ndarray, shape

The number of coefficients in the second dimension for each coefficient type at each level. contains the number of coefficients in the second dimension (for each coefficient type computed) at the ()th level of resolution, for .

dwtlvfrint, ndarray, shape

The number of coefficients in the third dimension for each coefficient type at each level. contains the number of coefficients in the third dimension (for each coefficient type computed) at the ()th level of resolution, for .

Raises
NagValueError
(errno )

On entry, .

Constraint: , the value of on initialization (see dim3_init()).

(errno )

On entry, .

Constraint: , the value of on initialization (see dim3_init()).

(errno )

On entry, .

Constraint: , the value of on initialization (see dim3_init()).

(errno )

On entry, and in dim3_init().

Constraint: in dim3_init().

(errno )

On entry, .

Constraint: .

(errno )

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

(errno )

Either the initialization function was called with or the communication array [‘icomm’] has been corrupted.

Notes

dim3_multi_fwd computes the multi-level DWT of three-dimensional data. For a given wavelet and end extension method, dim3_multi_fwd will compute a multi-level transform of a three-dimensional array , using a specified number, , of levels. The number of levels specified, , must be no more than the value returned in by the initialization function dim3_init() for the given problem. The transform is returned as a set of coefficients for the different levels (packed into a single array) and a representation of the multi-level structure.

The notation used here assigns level to the input data, . Level 1 consists of the first set of coefficients computed: the seven sets of detail coefficients are stored at this level while the approximation coefficients are used as the input to a repeat of the wavelet transform at the next level. This process is continued until, at level , all eight types of coefficients are stored. All coefficients are packed into a single array.

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)