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Multilevel 3-D wavelet reconstruction
X = waverec3(WDEC)
C = waverec3(WDEC,TYPE,N)
X = waverec3(WDEC,'a',0)
X
= waverec3(WDEC,'ca',0)
C = waverec3(WDEC,TYPE)
C
= waverec3(WDEC,TYPE,N)
waverec3 performs a multilevel 3-D wavelet reconstruction starting from a multilevel 3-D wavelet decomposition.
X = waverec3(WDEC) reconstructs the 3-D array X based on the multilevel wavelet decomposition structure WDEC. You can also use waverec3 to extract coefficients from a 3-D wavelet decomposition.
WDEC is a structure with the fields shown in the table.
C = waverec3(WDEC,TYPE,N) reconstructs the multilevel components at level N of a 3-D wavelet decomposition. N must be a positive integer less than or equal to the level of the decomposition.
Valid values for TYPE are:
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') is a low-pass filter and 'D' (or 'H') is a high-pass filter.
The char 'd' (or 'h' or 'D' or 'H') gives the sum of all the components different from the low-pass.
The char 'a' (or 'l' or 'A' or 'L') gives the low-pass component (the approximation at level N).
For extraction, the valid values for TYPE are the same but prefixed by 'c' or 'C'.
X = waverec3(WDEC,'a',0) or X = waverec3(WDEC,'ca',0) is equivalent to X = waverec3(WDEC). X is a reconstruction of the coefficients in WDEC at level 0.
C = waverec3(WDEC,TYPE) is equivalent to C = waverec3(WDEC,TYPE,N) with N equal to the level of the decomposition.
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, and HiR, which contain the filters used for 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 |