wd3D               package:wavethresh               R Documentation

_T_h_r_e_e-_d_i_m_e_n_s_i_o_n_a_l _d_i_s_c_r_e_t_e _w_a_v_e_l_e_t _t_r_a_n_s_f_o_r_m

_D_e_s_c_r_i_p_t_i_o_n:

     This function performs the 3D version of Mallat's discrete wavelet
     transform (see Mallat, 1989, although this paper does not describe
     in detail the 3D version the extension is trivial). The function
     assumes _periodic_ boundary conditions.

_U_s_a_g_e:

     wd3D(a, filter.number=10, family="DaubLeAsymm")

_A_r_g_u_m_e_n_t_s:

       a: A three-dimensional array constructed using the S-Plus
          'array()' function. Each dimension of the array should be
          equal to the same power of two.

filter.number: This selects the smoothness of wavelet that you want to
          use in the decomposition. By default this is 10, the
          Daubechies least-asymmetric orthonormal compactly supported
          wavelet with 10 vanishing moments.

  family: specifies the family of wavelets that you want to use. Two
          popular options are "DaubExPhase" and "DaubLeAsymm" but see
          the help for 'filter.select' for more possibilities.

_D_e_t_a_i_l_s:

     This function implements a straightforward extension of Mallat's,
     (1989) one- and two-dimensional DWT. The algorithm recursively
     applies all possible combinations of the G and H detail and
     smoothing filters to each of the dimensions thus forming 8
     different sub-blocks which we label HHH, GHH, HGH, GGH, HHG, GHG,
     HGG, and GGG. The algorithm recurses on the HHH component of each
     level (these are the father wavelet coefficients). 

     Making an analogy to the 2D transform where HH, HG, HG and GG is
     produced at each resolution level: the HG and GH correspond to
     "horizontal" and "vertical" detail and GG corresponds to "diagonal
     detail". The GGG corresponds to the 3D "diagonal" version, HGG
     corresponds to smoothing in dimension 1 and "diagonal" detail in
     dimensions 2 and 3, and so on. I don't think there are words in
     the English language which adequately describe "diagonal" in 3D -
     maybe cross detail?

_V_a_l_u_e:

     An object of class 'wd3D'.

_R_E_L_E_A_S_E:

     Version 3.9.6 Copyright Guy Nason 1997

_S_e_e _A_l_s_o:

     'wd', 'imwd', 'accessD.wd3D', 'print.wd3D', 'putD.wd3D',
     'putDwd3Dcheck', 'summary.wd3D', 'threshold.wd3D', 'wd3D.object',
     'wr3D'.

_E_x_a_m_p_l_e_s:

     #
     # Generate some test data: 512 standard normal observations in an 8x8x8
     # array.
     #
     #test.data.3D <- array(rnorm(8*8*8), dim=c(8,8,8))
     #
     # Now do the 3D wavelet transform
     #
     #tdwd3D <- wd3D(test.data.3D)
     #
     # See example explaining  the 3D wavelet transform.
     #

