GSP_PYRAMID_SYNTHESIS - Synthesizes a signal from its graph pyramid transform coefficients

Usage

reconstruction=gsp_pyramid_synthesis(Gs,coarsest_approximation,prediction_errors);
reconstruction=gsp_pyramid_synthesis(Gs,coarsest_approximation,prediction_errors,param);

Input parameters

`Gs`	A multiresolution sequence of graph structures, including the idx parameters tracking the subsampling pattern.
`coarsest_approximation`
	The coarsest approximation of the original signal.
`prediction_errors`
	Cell array with the prediction errors at each level.

Output parameters

`reconstruction`	The synthesized signal.
`coarse_approximations`
	Sequence of coarse approximations

Description

'gsp_pyramid_synthesis(Gs,coarsest_approximation,prediction_errors)' synthesizes a signal from its graph pyramid transform coefficients.

param is a structure containing optional arguments including

param.regularize_epsilon : Interpolation parameter.
param.least_squares : Set to 1 to use the least squares synthesis (default=0)
param.use_landweber : Set to 1 to use the Landweber iteration approximation in the least squares synthesis.
param.landweber_its : Number of iterations in the Landweber approximation for least squares synthesis.
param.landweber_tau : Parameter for the Landweber iteration.
param.h_filters : A cell array of graph spectral filters. If just one filter is included, it is used at every level of the pyramid. These filters are required for least squares synthesis, but not for the direct synthesis method Default

\begin{equation*} h(x) = \frac{0.5}{0.5+x} \end{equation*}

Please read the documentation of gsp_filter_analysis for other optional arguments.

Demo: gsp_demo_pyramid

References:

D. I. Shuman, M. J. Faraji, and P. Vandergheynst. A framework for multiscale transforms on graphs. arXiv preprint arXiv:1308.4942, 2013.