cthresh               package:cthresh               R Documentation

_E_s_t_i_m_a_t_e _r_e_a_l _s_i_g_n_a_l _u_s_i_n_g _c_o_m_p_l_e_x-_v_a_l_u_e_d _w_a_v_e_l_e_t_s

_D_e_s_c_r_i_p_t_i_o_n:

     Implements the multiwavelet style and empirical Bayes shrinkage
     procedures described in Barber & Nason (2004)

_U_s_a_g_e:

     cthresh(data, j0 = 3, dwwt, dev = madmad, rule = "hard", 
         filter.number = 3.1, family = "LinaMayrand", plotfn = FALSE,  
         TI = FALSE, details = FALSE, policy = "mws", code = "NAG", tol = 0.01)

_A_r_g_u_m_e_n_t_s:

    data: The data to be analysed. This should be real-valued and of
          length a power of two.

      j0: Primary resolution level; no thresholding is done below this
          level.

    dwwt: description to come

     dev: A function to be used to estimate the noise level of the
          data. The function supplied must return a value of spread on
          the variance scale (i.e. not standard deviation) such as the
          var() function. A popular, useful and robust alternative is
          the madmad function.

    rule: The type of thresholding done. If policy = "mws", available
          rules are "hard" or "soft"; if policy = "ebayes", then rule
          can be "hard", "soft" or "mean".

filter.number, family: These parameters specify the wavelet used. See
          'filter.select' for details. 

          Also, if filter.number = 5, estimation is done with all the
          complex-valued wavelets with 5 vanishing moments and the
          results averaged. If filter.number = 0, then he averaging is
          over all available complex-valued wavelets.

  plotfn: If 'plotfn = true', then a plot of the noisy data and
          estimated signal are produced.

      TI: If TI = T, then the non-decimated transform is used. See the
          help pages for wd and wst for more on the non-decimated
          transform.

 details: If 'details = FALSE' (the default), only the estimate of the
          underlying signal is returned. If 'details = TRUE', many
          other details are also returned.

  policy: Controls the type of thresholding done. Available policies
          are multiwavelet style (policy = "mws") and empirical Bayes
          (policy = "ebayes").

    code: Tells cthresh whether external C or NAG code is available to
          help with the calculations.

     tol: A tolerance parameter used in searching for prior parameters
          if the empirical Bayes policy is used.

_D_e_t_a_i_l_s:

     If a real-valued signal is decomposed using a complex-valued
     wavelet (like the Lina-Mayrand wavelets supplied by
     filter.select), then the wavelet coefficients are also
     complex-valued. Wavelet shrinkage can still be used to estimate
     the signal, by asking the question "which coefficients are small
     (and represent noise) and which are large (and represent signal)?"
     Two methods of determining which coefficients are small and which
     are large are proposed by Barber & Nason (2004). One is
     "multiwavelet style" thresholding (similar to that in Downie &
     Silverman (1998) where the coefficients are treated like the
     coefficients of a multiwavelet. Here, the "size" of the wavelet
     coefficient is determined as modulus of a standardised version of
     the coefficient. The standardisation is by the square root of the
     covariance matrix of the coefficient. A Bayesian method is to
     place a mixture prior on each coefficient. The prior has two
     components: a bivariate normal and a point mass at (0,0). The
     parameters are determined by an empirical Bayes argument and then
     the prior is updated by the data.

_V_a_l_u_e:

     Either a vector containing the estimated signal (if details =
     FALSE), or a list with the following components:  

    data: The original data as supplied to cthresh.

 data.wd: The wavelet decomposition of the data.

  thr.wd: The thresholded version of data.wd.

estimate: The estimate of the underlying signal.

   Sigma: The covariance matrices induced by the wavelet transform. See
          'make.dwwt' for more details.

   sigsq: The estimate of the variance of the noise which corrupted the
          data.

    rule: Which thresholding rule was used

  EBpars: The empirical Bayes parameters found by the function
          find.parameters. Only present if the "ebayes" policy was
          used.

 wavelet: A list with components filter.number and family which, when
          supplied to 'link{filter.select}', determine the wavelet used
          to decompose the data.

_R_E_L_E_A_S_E:

     Part of the CThresh addon to WaveThresh. Copyright Stuart Barber
     and Guy Nason 2004.

_N_o_t_e:

     The estimates returned by cthresh have an imaginary component. In
     practice, this component is usually negligible.

_S_e_e _A_l_s_o:

     'filter.select', 'find.parameters', 'link{make.dwwt}',
     'test.data', and the undocumented functions in CThresh.

