Function INVERSE_SCAT

Package

Short description

Usage

    xt = inverse_scat(S, filters, options, node)

Input

    S (cell): The scattering coefficients output by SCAT.
    filters (cell): The set of filter banks used to calculate S. Can be
        obtained from FILTER_BANK or second output of WAVELET_FACTORY_1D.
    options (struct, optional): Specifies different parameters for the 
        inversion. These are passed on to GRIFFIN_LIM and RICHARDSON_LUCY, so
        please see the documentation for these functions for specific 
        parameter settings.
    node (numeric, optional): A vector of the form [m p], where m is the 
        coefficient to recover and p is its index. If [S,U] is the output of
        the SCAT function, this corresponds to estimating U{m+1}.singal{p}.
        To recover the original signal, node is therefore [0 1] (Default 
        [0 1])

Output

    xt (numeric): The reconstructed signal.

Description

    The scattering transform is inverted recursively, estimating 
    U{m+1}.signal{p} for each layer, starting with the last and propagating
    upwards until U{1}.signal{1} is obtained, which is an estimate of the 
    original signal.
    For the last layer m = l, the Richardson-Lucy deconvolution algorithm is 
    applied to estimate U{l+1}.signal{p} from S{l+1}.signal{p}. Previous
    layers are reconstructed through the Griffin & Lim algorithm, with the
    estimate of U{m+1}.signal{p1} are obtained from the estimates of 
    U{m+2}.signal{p2}, where p2 correspond to the wavelet modulus coeffi-
    cients in layer m+1 of the coefficient p1 in layer m -- the former being
    the "children" of the latter.

See also

• griffin_lim
• inverse_wavelet_1d
• richardson_lucy