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Multilevel 3-D wavelet decomposition
WDEC = wavedec3(X,N,'wname')
WDEC = wavedec3(X,N,'wname','mode','ExtM')
WDEC = wavedec3(X,N,{LoD,HiD,LoR,HiR})
wavedec3 is a three-dimensional wavelet analysis function.
WDEC = wavedec3(X,N,'wname') returns the wavelet decomposition of the 3-D array X at level N, using the wavelet named in string 'wname' or the particular wavelet filters you specify. It uses the default extension mode 'sym'. See dwtmode. N must be a positive integer.
WDEC = wavedec3(X,N,'wname','mode','ExtM') uses the specified DWT extension mode .
WDEC = wavedec3(X,N,{LoD,HiD,LoR,HiR}) uses the decomposition and reconstruction filters you specify in a cell array.
WDEC is the output decomposition structure, with the following fields:
sizeINI | Size of the three-dimensional array X |
level | Level of the decomposition |
mode | Name of the wavelet transform extension mode |
filters | Structure with 4 fields, LoD, HiD, LoR, HiR, which contain the filters used for the DWT. |
dec | N x 1 cell array containing the coefficients of the decomposition. N is equal to 7*WDEC.level+1. dec{1} contains the lowpass component (approximation) at the level of the decomposition. The approximation is equivalent to the filtering operations 'LLL'. dec{k+2},...,dec{k+8} with k = 0,7,14,...,7*(WDEC.level-1) contain the 3-D wavelet coefficients for the multiresolution starting with the coarsest level when k=0. For example, if WDEC.level=3, dec{2},...,dec{8} contain the wavelet coefficients for level 3 (k=0), dec{9},...,dec{15} contain the wavelet coefficients for level 2 (k=7), and dec{16},...,dec{22} contain the wavelet coefficients for level 1 (k=7*(WDEC.level-1)). At each level, the wavelet coefficients in dec{k+2},...,dec{k+8} are in the following order: 'HLL','LHL','HHL','LLH','HLH','LHH','HHH'. The strings give the order in which the separable filtering operations are applied from left to right. For example, 'LHH' means that the lowpass (scaling) filter with downsampling is applied to the rows of X, followed by the highpass (wavelet) filter with downsampling applied to the columns of X. Finally, the highpass filter with downsampling is applied to the 3rd dimension of X. |
sizes | Successive sizes of the decomposition components |