wstCVl              package:wavethresh              R Documentation

_P_e_r_f_o_r_m_s _t_w_o-_f_o_l_d _c_r_o_s_s-_v_a_l_i_d_a_t_i_o_n _e_s_t_i_m_a_t_i_o_n _u_s_i_n_g _p_a_c_k_e_t-_o_r_d_e_r_e_d _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_s _a_n_d _a (_v_e_c_t_o_r) _l_e_v_e_l-_d_e_p_e_n_d_e_n_t _t_h_r_e_s_h_o_l_d.

_D_e_s_c_r_i_p_t_i_o_n:

     Performs Nason's 1996 two-fold cross-validation estimation using
     packet-ordered non-decimated wavelet transforms and a (vector)
     level-dependent threshold.

_U_s_a_g_e:

     wstCVl(ndata, ll = 3, type = "soft", filter.number = 10, family = "DaubLeAsymm",
             tol = 0.01, verbose = 0, plot.it = FALSE, norm = l2norm, InverseType = "average",
             uvdev = madmad)

_A_r_g_u_m_e_n_t_s:

   ndata: the noisy data. This is a vector containing the signal plus
          noise. The length of this vector should be a power of two.

      ll: the primary resolution for this estimation. Note that the
          primary resolution is _problem-specific_: you have to find
          out which is the best value.

    type: whether to use hard or soft thresholding. See the explanation
          for this argument in the 'threshold.wst' function.

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. The
          options are "DaubExPhase" and "DaubLeAsymm".

     tol: the cross-validation tolerance which decides when an estimate
          is sufficiently close to the truth (or estimated to be so).

 verbose: If 'TRUE' then informative messages are printed during the
          progression of the function, otherwise they are not.

 plot.it: 

    norm: which measure of distance to judge the dissimilarity between
          the estimates. The functions 'l2norm' and 'linfnorm' are
          suitable examples.

InverseType: The possible options are "average" or "minent". The former
          uses basis averaging to form estimates of the unknown
          function. The "minent" function selects a basis using the
          Coifman and Wickerhauser, 1992 algorithm to select a basis to
          invert.

   uvdev: Universal thresholding is used to generate an upper bound for
          the ideal threshold. This argument provides the function that
          computes an estimate of the variance of the noise for use
          with the universal threshold calculation (see
          'threshold.wst').

_D_e_t_a_i_l_s:

     This function implements a modified version of the
     cross-validation method detailed by Nason, 1996 for computing an
     estimate of the error between an estimate and the ``truth''. The
     difference here is that it uses the packet ordered non-decimated
     wavelet transform rather than the standard Mallat wd discrete
     wavelet transform. As such it is an example of the
     translation-invariant denoising of Coifman and Donoho, 1995 but
     uses cross-validation to choose the threshold rather than
     SUREshrink. 

     Further, this function computes level-dependent thresholds. That
     is, it can compute a different threshold for each resolution
     level. 

     Note that the procedure outlined above can use 'AvBasis' basis
     averaging or basis selection and inversion using the Coifman and
     Wickerhauser, 1992 best-basis algorithm

_V_a_l_u_e:

     A list returning the results of the cross-validation algorithm.
     The list includes the following components: 

   ndata: a copy of the input noisy data

    xvwr: a reconstruction of the best estimate computed using this
          algorithm. It is the inverse (computed depending on what the
          InverseType argument was) of the 'xvwrWSTt' component.

xvwrWSTt: a thresholded version of the packet-ordered non-decimated
          wavelet transform of the noisy data using the best threshold
          discovered by this cross-validation algorithm.

     uvt: the universal threshold used as the upper bound for the
          algorithm that tries to discover the optimal cross-validation
          threshold. The lower bound is always zero.

xvthresh: the best threshold as discovered by cross-validation. Note
          that this is vector, a level-dependent threshold with one
          threshold value for each resolution level. The first entry
          corresponds to level 'll', the last entry corresponds to
          level 'nlevels(ndata)-1' and the entries in between linearly
          to the levels in between. The 'wstCV' function should be used
          to compute a global threshold.

  optres: The results from performing the optimisation using the
          'nlminb' function from Splus. This object contains many
          interesting components with information about how the
          optimisation went. See the 'nlminb' help page for
          information.

_R_E_L_E_A_S_E:

     Version 3.6 Copyright Guy Nason 1995

_S_e_e _A_l_s_o:

     'GetRSSWST', 'linfnorm', 'linfnorm', 'threshold.wst', 'wst',
     'wst.object', 'wstCV'

_E_x_a_m_p_l_e_s:

     #
     # Example PENDING
     #

