denoiseheteroprop           package:adlift           R Documentation

_d_e_n_o_i_s_e_h_e_t_e_r_o_p_r_o_p

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

     Denoises the inputted signal using artificial levels noise
     variance estimation and bayesian thresholding, assuming noise
     variances known up to proportionality constants.

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

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

_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). 

  gamvec: a vector of proportions of the noise standard deviations (in
          the order of 'x').

_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 normalising factors are calculated assuming that the noise
     associated to the ith gridpoint is gamma_{i}sigma. The
     coefficients are divided into artificial levels, and the first
     (largest)level is used to estimate the noise variance of the
     coefficients.  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.

_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',

_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
     gvec<-c(rep(.4,times=100),rep(.7,times=100),rep(.3,times=56))
     #
     est1<-denoiseheteroprop(x1,z1,AdaptNeigh,1,TRUE,TRUE,2,"median",gvec)
     sum(abs(y1-est1$fhat$coeff))
     #
     #the error between the true signal and the denoised version. 

