wstCV               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 _o_n_e, _g_l_o_b_a_l, _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 one, global,
     threshold.

_U_s_a_g_e:

     wstCV(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: If 'TRUE' then a plot of the progress of optimising the error
          estimate for different values of the threshold is generated
          as the algorithm proceeds. The algorithm tries to minimize
          the error estimate so you should see a ``bowl'' developing.
          After each iteration the error estimate is plotted with the
          iteration number so you should see the numbers tend to the
          bottom of the bowl.

    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 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. 

     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 one number, the global threshold. The 'wstCVl'
          function should be used to compute a level-dependent
          threshold. 

   xkeep: a vector containing the various thresholds used by the
          optimisation algorithm in trying to determine the best one.
          The length of this vector cannot be pre-determined but
          depends on the noisy data, thresholding method, and
          optimisation tolerance. 

   fkeep: a vector containing the value of the estimated error used by
          the optimisation algorithm in trying to minimize the
          estimated error. The length, like that of xkeep cannot be
          predetermined for the same reasons.

_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', 'wstCVl'.

_E_x_a_m_p_l_e_s:

     #
     # Example PENDING
     #

