denoisehetero             package:adlift             R Documentation

_d_e_n_o_i_s_e_h_e_t_e_r_o

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

     Denoises the inputted signal using artificial levels noise
     variance estimation and bayesian thresholding, using
     heteroscedastic (estimated) noise variances.

_U_s_a_g_e:

     denoisehetero(x, f, pred, neigh, int, clo, keep, rule = "median")

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

       x: A vector of grid values. Can be of any length, not
          necessarily equally spaced. 

       f: A vector of function values corresponding to 'x'. Must be of
          the same length as 'x'.

    pred: The type of regression to be performed. Possible options are
          'LinearPred', 'QuadPred', 'CubicPred', 'AdaptPred' and
          'AdaptNeigh'.

   neigh: The number of neighbours over which the regression is
          performed at each step. If clo is false, then this in fact
          denotes the number of neighbours on each side of the removed
          point.

     int: Indicates whether or not the regression curve includes an
          intercept.

     clo: Refers to the configuration of the chosen neighbours. If
          'clo' is false, the neighbours will be chosen symmetrically
          around the removed point. Otherwise, the closest neighbours
          will be chosen.

    keep: The number of scaling coefficients to be kept in the final
          representation of the initial signal. This must be at least
          two.

    rule: The type of bayesian thresholding used in the procedure.
          Possible values are '"mean"', '"median"' (posterior mean or
          median thresholding) or "hard or "soft" (hard or soft
          thresholding). 

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

     The function uses the transform matrix to normalise the detail
     coefficients produced from the forward transform, so that they can
     be used in the bayesian thresholding procedure 'ebayesthresh'. The
     coefficients are divided into artificial levels, and the first
     (largest)level is used to estimate the noise variances of the
     coefficients, based on the MAD of those coefficients falling in a
     sliding window around each gridpoint.  Ebayesthresh is then used
     to threshold the coefficients. The resulting new coefficients are
     then unnormalised and the transform inverted to obtain an estimate
     of the true (unnoisy) signal.

_V_a_l_u_e:

     out: the output from the forward transform.

       w: the matrix associated to the wavelet transform.

   indsd: the individual coefficient variances introduced by the
          transform.

      al: the artificial levels used to estimate the noise variance.

      sd: the standard deviation of the noise.

    fhat: the estimate of the function after denoising.

   fhat1: the estimate of the function after denoising, using the
          alternate variance estimate of MAD, centered at zero.

   fhat2: the estimate of the function after denoising, using the
          alternate variance estimate of the median of the absolute
          values of the detail coefficients.

_A_u_t_h_o_r(_s):

     Matt Nunes (matt.nunes@bristol.ac.uk), Marina Popa
     (Marina.Popa@bristol.ac.uk)

_S_e_e _A_l_s_o:

     'denoise', 'ebayesthresh', 'heterovar'

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

     x1<-runif(256)
     y1<-make.signal2("doppler",x=x1)
     n1<-rnorm(256,0,.1)
     z1<-y1+n1
     #
     est1<-denoisehetero(x1,z1,AdaptNeigh,1,TRUE,TRUE,2)
     sum(abs(y1-est1$fhat$coeff))
     #
     #the error between the true signal and the denoised version. 

