mwr                package:wavethresh                R Documentation

_M_u_l_t_i_p_l_e _d_i_s_c_r_e_t_e _w_a_v_e_l_e_t _t_r_a_n_s_f_o_r_m (_r_e_c_o_n_s_t_r_u_c_t_i_o_n).

_D_e_s_c_r_i_p_t_i_o_n:

     This function performs the reconstruction stage of Mallat's
     pyramid algorithm adapted for multiple wavelets (see Xia et
     al.(1996)), i.e. the discrete inverse _multiple_ wavelet
     transform.

_U_s_a_g_e:

     mwr(mwd, prefilter.type = mwd$prefilter, verbose = FALSE, start.level = 0,
             returnC = FALSE)

_A_r_g_u_m_e_n_t_s:

     mwd: A multiple wavelet decomposition object as returned by 'mwd'.

prefilter.type: Usually best not to change this (i.e. not to use a
          different prefilter on the reconstruction to the one used on
          decomposition).

 verbose: Controls the printing of "informative" messages whilst the
          computations progress. Such messages are generally annoying
          so it is turned off by default.

start.level: The level you wish to start reconstruction at. The is
          usually the first (level 0).

 returnC: If this is FALSE then a vector of the same length as the
          argument data supplied to the function 'mwd' that constructed
          the supplied 'mwd.object'. is returned, Ie. the reconstructed
          data. If true then the last level (highest resolution) C
          coefficients are returned in matrix form. This matrix has not
          been postprocessed. 

_D_e_t_a_i_l_s:

     The code implements Mallat's pyramid algorithm adapted for
     multiple wavelet decompositions (Xia et al. 1996). In the
     reconstruction the quadrature mirror filters G and H are supplied
     with C0 and D0, D1, ... D(J-1) (the wavelet coefficients) and
     rebuild C1,..., CJ. 

     The matrix CJ is postprocessed which returns the full
     reconstruction 

     If 'mwd.object' was obtained directly from 'mwd' then the original
     function can be reconstructued exactly. Usually, the 'mwd.object'
     has been modified in some way, for example, some coefficients set
     to zero by 'threshold'. Mwr then reconstructs the function with
     that set of wavelet coefficients. 

     See also Downie and Silverman, 1998

_V_a_l_u_e:

     Either a vector containing the final reconstruction or a matrix
     containing unpostprocessed coefficients.

_R_E_L_E_A_S_E:

     Version 3.9.6 (Although Copyright Tim Downie 1996)

_S_e_e _A_l_s_o:

     'accessC.mwd', 'accessD.mwd', 'draw.mwd', 'mfirst.last',
     'mfilter.select', 'mwd', 'mwd.object', 'plot.mwd', 'print.mwd',
     'putC.mwd', 'putD.mwd', 'summary.mwd', 'threshold.mwd', 'wd',
     'wr.mwd'.

_E_x_a_m_p_l_e_s:

     #
     # Decompose and then exactly reconstruct test.data
     #
     #tdecomp <- mwd(test.data)
     #trecons <- mwr(tdecomp)
     #
     # Look at accuracy of reconstruction
     # max(abs(trecons - test.data))
     #[1] 2.266631e-12
     #
     # See also the example of using this-is-escaped-codenormal-bracket68bracket-normal or mwr in
     # the this-is-escaped-codenormal-bracket70bracket-normal section of
     # the help for this-is-escaped-codenormal-bracket72bracket-normal.

