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GSP_DESIGN_MEXICAN_HAT - Design the mexican hat filterbank

Usage

g =  gsp_design_mexican_hat(G, Nf, param);
gsp_design_mexican_hat(G ,Nf);
gsp_design_mexican_hat(G);

Input parameters

G Graph or upper bound on the Laplacian spectrum
Nf Number of filters to cover the interval [0,lmax] (default 6)
param Structure of optional parameters

Output parameters

g A cell array of filters

Description

This function return a array of filters designed to be mexican hat wavelet. The mexican hat wavelet is the second oder derivative of a Gaussian. Since we express the filter in the Fourier domain, we find:

In our convention the eigenvalues of Laplacian are equivalent to the square of vertex frequencies: \(f = \lambda^2\).

The low pass filter is given by

param is an optional structure containing the following fields

  • param.t: vector of scale to be used (default: log scale)
  • param.lpfactor: lmin*=*lmax/lpfactor will be used to determine scales, then scaling function kernel will be created to fill the lowpass gap. (default 20)
  • param.verbose: verbosity level. 0 no log - 1 display warnings. (default 1)
  • param.normalize: normalize the wavelet by the factor \(\sqrt{t}\) (default 0.)

This function will compute the maximum eigenvalue of the laplacian. To be more efficient, you can precompute it using:

G = gsp_estimate_lmax(G);

Example:

Nf = 8;
G = gsp_sensor(100);
G = gsp_estimate_lmax(G);
g = gsp_design_mexican_hat(G, Nf);
gsp_plot_filter(G,g);
gsp_design_mexican_hat_1_1.png

This function is inspired by the sgwt_toolbox.