

imwd(wavethresh)                             R Documentation

_2_D _D_i_s_c_r_e_t_e _W_a_v_e_l_e_t _T_r_a_n_s_f_o_r_m _(_I_m_a_g_e _W_. _D_e_c_o_m_p_o_s_i_t_i_o_n_)

_D_e_s_c_r_i_p_t_i_o_n_:

     This function performs the decomposition stage of Mal-
     lat's pyramid algorithm i.e. the discrete wavelet
     transform for images.

_U_s_a_g_e_:

     imwd(image, filter.number=2, bc="periodic", verbose=FALSE)

_A_r_g_u_m_e_n_t_s_:

   image: Square matrix containing the image. The number of
          rows in the image must be a power of 2. Since the
          matrix is square, this is also the number of
          columns in the matrix.

filter.number: The filter that you wish to use to decompose
          the function. The filters are obtained from the
          "filter.select" function and are the compactly
          supported orthonormal wavelets as described in
          Daubechies, I.

      bc: boundary treatment. The periodic (default) treat-
          ment causes the decomposition to act as if the
          function you are trying to decompose is periodic
          (on it's own interval). The other option is sym-
          metric, which used to be the default. This causes
          the decomposition to act as if the function
          extended by symmetric reflection at each end.

 verbose: logical; if true then informative messages are
          printed whilst the computations are performed.

_D_e_t_a_i_l_s_:

     The 2D algorithm is essentially the application of many
     1D filters.  First, the columns are attacked with the
     smoothing (H) and bandpass (G) filters, and the rows of
     each of these resultant images are attacked again with
     each of G and H, this results in 4 images.  Three of
     them, GG, GH, and HG correspond to the highest resolu-
     tion wavelet coefficients. The HH image is a smoothed
     version of the original and can be further attacked in
     exactly the same way as the original image to obtain
     GG(HH), GH(HH), and HG(HH), the wavelet coefficients at
     the second highest resolution level and HH(HH) the
     twice-smoothed image, which then goes on to be further
     attacked.

     After each attack the dimension of the images is
     halved.  After many attacks you will obtain four real
     numbers, one of which correspond to the image smoothed
     many times.

     Exact details of the algorithm are to be found in Mal-
     lat 1989.

_V_a_l_u_e_:

     An object of class "imwd", a list containing the
     wavelet coefficients (see "imwd.object").

_E_x_a_m_p_l_e_s_:

     # Do a decomposition of an image
     #
     data(lennon)
     imwdL <- imwd(lennon)
     # Look at the coefficients --> example(plot.imwd)

