idwt3

Single-level 3-D inverse discrete wavelet transform

Syntax

X = idwt3(wt)

C = idwt3(wt,type)

Description

X = idwt3(wt) returns the single-level reconstructed 3-D array X based on the single-level three-dimensional wavelet decomposition structure wt.

C = idwt3(wt,type) returns the single-level reconstructed component of specified type.

Examples

Single-Level Three-Dimensional Wavelet Reconstruction

Create a 3-D array.

X  = reshape(1:64,4,4,4);
tiledlayout(2,2)
for k=1:4
    nexttile
    imagesc(X(:,:,k))
    title("k = "+num2str(k))
    colorbar
end

Decompose X using the Haar wavelet.

wt = dwt3(X,"haar");

Reconstruct X from the coefficients. Verify that the reconstructed data agrees with the original data to machine precision.

XR = idwt3(wt);

dff = max(abs(X(:)-XR(:)))

dff = 
3.5527e-14

Compute the reconstructed approximation, which consists of the lowpass component.

A  = idwt3(wt,"aaa");

Compute the sum of all the components different from the lowpass component. Visualize the reconstruction.

D  = idwt3(wt,"d");
tiledlayout(2,2)
for k=1:4
    nexttile
    imagesc(D(:,:,k))
    title("k = "+num2str(k))
    colorbar
end

Reconstruct the component associated with lowpass in the x and z directions and highpass in the y direction.

ADA  = idwt3(wt,"ada");

Input Arguments

wt — Single-level 3-D wavelet decomposition

structure

Single-level 3-D wavelet decomposition, specified as a structure with these fields:

sizeINI	Size of the three-dimensional array X.
mode	Name of the wavelet transform extension mode.
filters	Structure with four fields: LoD, HiD, LoR, HiR, which are the filters used for DWT.
dec	2-by-2-by-2 cell array containing the coefficients of the decomposition. dec{i,j,k}, where i, j, and k equal 1 or 2, contains the coefficients obtained by lowpass filtering (for i, j, or k equal to 1) or highpass filtering (for i, j, k equal to 2). The i element filters along the rows of X, the j element filters along the columns, and the k element filters along the third dimension. For example, dec{1,2,1} is obtained by filtering X along the rows with the lowpass (scaling) filter, along the columns with the highpass (wavelet) filter, and along the third dimension with the lowpass (scaling) filter.

type — Type of reconstruction

character vector | string scalar

Type of reconstruction, specified as a character vector or string scalar. Valid values of type are these:

• A group of three characters 'xyz', one per direction, with each character selected in the set {'a', 'd', 'l', 'h'} or in the corresponding uppercase set {'A','D', 'L', 'H'}, where 'A' (or 'L') is a lowpass filter and 'D' (or 'H') is a highpass filter.

• The char 'd' (or 'h' or 'D' or 'H') gives the sum of all the components different from the lowpass component.

Data Types: char | string

Output Arguments

X — Reconstruction

3-D array

Reconstruction, returned as a 3-D array.

C — Reconstructed component

3-D array

Reconstructed component of specified type, returned as a 3-D array.

Version History

Introduced in R2010a