wst2D.object           package:wavethresh           R Documentation

(_P_a_c_k_e_t _o_r_d_e_r_e_d) _T_w_o-_d_i_m_e_n_s_i_o_n_a_l _n_o_n_d_e_c_i_m_a_t_e_d _w_a_v_e_l_e_t _t_r_a_n_s_f_o_r_m _d_e_c_o_m_p_o_s_i_t_i_o_n _o_b_j_e_c_t_s.

_D_e_s_c_r_i_p_t_i_o_n:

     These are objects of class 'wst2D' They represent a decomposition
     of a function with respect to a set of (all possible) shifted
     two-dimensional wavelets. They are a 2D extension of the
     'wst.object'.

_D_e_t_a_i_l_s:

     To retain your sanity we recommend that the coefficients from a
     'wst2D' object be extracted or replaced using 

     \textbullet{'getpacket.wst2D' to obtain individual packets of
     either father or mother wavelet coefficients.}
     \textbullet{'putpacket.wst2D' to insert coefficients.}

     You can obtain the coefficients directly from the 'wst2D$wst2D'
     component but you have to understand their organization described
     above.

_V_a_l_u_e:

     The following components must be included in a legitimate 'wst2D'
     object.  

   wst2D: This a three-dimensional array. Suppose that the original
          image that created the 'wst2D' object is n x n. Then the
          dimension of the 'wst2D' array is [ nlevels, 2n, 2n]. The
          first index of the array refers to the resolution level of
          the array with "resolution level = index - 1" (so, e.g. the
          coarsest scale detailed is stored at index 1 and the finest
          at index nlevels). For a given resolution level (selected
          first index) the associated 2n x 2n matrix contains the
          two-dimensional non-decimated wavelet coefficients for that
          level packed as follows. 

          At the finest resolution level the 2n x 2n coefficient image
          may be broken up into four n x n subimages. Each of the four
          images corresponds to data shifts in the horizontal and
          vertical directions. The top left image corresponds to ``no
          shift'' and indeed the top left image corresponds to the
          coefficients obtained using the decimated 2D wavelet
          transform as obtained using the 'imwd' function. The top
          right image corresponds to a horizontal data shift; the
          bottom left to a vertical data shift and the bottom right
          corresponds to both horizontal and vertical data shift. 

          Within each of the four n x n images named in the previous
          paragraph are again 4 subimages each of dimension n/2 x n/2.
          These correspond to (starting at the top left and moving
          clockwise) the smooth (CC), horizontal detail (DC), diagonal
          detail (DD) and vertical detail (CD). 

          At coarser resolution levels the coefficients are smaller
          submatrices corresponding to various levels of data shifts
          and types of detail (smooth, horizontal, vertical, diagonal). 

          We strongly recommend the use of the 'getpacket.wst2D' and
          'putpacket.wst2D' functions to remove and replace
          coefficients from 'wst2D'

 nlevels: The number of levels in the decomposition. If you raise 2 to
          the power of 2 'nlevels' you get the number of data points
          used in the decomposition.

  filter: a list containing the details of the filter that did the
          decomposition (equivalent to the return value from the
          'filter.select' function).

    date: The date that the transform was performed or the 'wst2D' was
          modified.

_G_E_N_E_R_A_T_I_O_N:

     This class of objects is returned from the 'wst2D' function which
     computes the _packets-ordered_ two-dimensional non-decimated
     wavelet transform (effectively all possible shifts of the standard
     two-dimensional discrete wavelet transform). 

     Many other functions return an object of class 'wst2D'.

_M_E_T_H_O_D_S:

     The wst2D class of objects has methods for the following generic
     functions: 'AvBasis', 'getpacket'. 'plot', 'print', 'putpacket',
     'summary',

_R_E_L_E_A_S_E:

     Version 3.5.3 Copyright Guy Nason 1994

_S_e_e _A_l_s_o:

     'wst2D'

