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idwt3

Single-level inverse discrete 3-D wavelet transform

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Syntax

X = idwt3(WT)
C = idwt3(WT,TYPE)

Description

Theidwt3command performs a single-level three-dimensional wavelet reconstruction starting from a single-level three-dimensional wavelet decomposition.

X = idwt3(WT)computes the single-level reconstructed 3-D array X, based on the three-dimensional wavelet decomposition stored in the WT structure. This structure contains the following fields.

sizeINI

Size of the three-dimensional arrayX.
mode

Name of the wavelet transform extension mode.
filters

Structure with 4 fields,LoD,HiD,LoR,HiR, which contain the filters used for DWT.
12月

2 x 2 x 2 cell array containing the coefficients of the decomposition.

12月{i,j,k},i,j,k = 1or2contains the coefficients obtained by low-pass filtering (foriorjork = 1) or high-pass filtering (foriorjork = 2).

C = idwt3(WT,TYPE)computes the single-level reconstructed component based on the three-dimensional wavelet decomposition. Valid values forTYPEare:

  • A group of three characters“xyz”, one per direction, with'x','y'and'z'selected in the set {'a','d','l','h'} or in the corresponding uppercase set {'A','D','L','H'}), where'A'(or'L') specifies low-pass filter and'D'(or'H') specifies highpass filter.

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

Examples

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Define the original 3-D data.

X = reshape(1:64,4,4,4)
X(:,:,1) = 1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16 X(:,:,2) = 17 21 25 29 18 22 26 30 19 23 27 31 20 24 28 32 X(:,:,3) = 33 37 41 45 34 38 42 46 35 39 43 47 36 40 44 48 X(:,:,4) = 49 53 57 61 50 54 58 62 51 55 59 63 52 56 60 64

DecomposeXusing“db1”.

wt = dwt3(X,“db1”);

ReconstructXfrom the coefficients. Verify that the reconstructed data agrees with the original data to machine precision.

XR = idwt3(wt); dff = max(abs(X-XR))
dff(:,:,1) = 1.0e-13 * 0.0266 0.0355 0.0888 0.1066 dff(:,:,2) = 1.0e-13 * 0.1066 0.1066 0.2132 0.2132 dff(:,:,3) = 1.0e-13 * 0.1421 0.1421 0.2132 0.2132 dff(:,:,4) = 1.0e-13 * 0.3553 0.3553 0.2842 0.2842

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.

D = idwt3(wt,'d');

Reconstruct the component associated with lowpass in thexandzdirections and highpass in they方向。

ADA = idwt3(wt,'ada');

See Also

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Introduced in R2010a

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