Scattering.m

a MATLAB toolbox for signal scattering

Scattering representations are based on nonlinear transforms which are invariant to translation and stable to deformations, yet remaining highly discriminative.

Usage

Suppose you have a signal sampled at rate Fs. Choose a quality factor (number of frequency bins per octave) Q and run default_auditory to get started with a time-frequency representation called scalogram, that is, wavelet transform modulus.

Q = 8; % typical values for quality factor in audio are 8, 12 or 16
opts{1} = default_auditory(length(signal),Fs,Q);

A scattering architecture adds a second layer of wavelet transform on top of the scalogram. This toolbox provides the ability to perform scattering along time (a.k.a. amplitude modulation spectrum), but also joint time-frequency scattering (introduced by Joakim Andén) and spiral scattering (introduced by Vincent Lostanlen).

% This line provides default options for scattering along time
opts{2}.time = struct();
% Uncomment this line to enable joint time-frequency scattering
% opts{2}.gamma = struct(); % gamma is the log-frequency variable
% Uncomment this line to enable spiral scattering
% opts{3}.j = struct(); % j is the octave variable

Run sc_setup to build the scattering architectures, which consist of filter banks and a nonlinearity (complex modulus by default). Then run sc_propagate to compute the scattering coefficients.

archs = sc_setup(opts);
S = sc_propagate(signal,archs);

If you want to change the default behavior, add specific fields to the empty structures in opts. See the documentation for available parameters.

Install

First, acquire the source code by cloning the git repository:

git clone git://github.com/lostanlen/scattering.m.git

Now, start MATLAB and add the toolbox to your local path:

addpath(genpath('path/to/scattering.m/lib'))

and start calling sc_setup and sc_propagate on your signals.

Documentation

Documentation can be browsed on Read The Docs.

License and contact

All files in the Scattering.m toolbox are licensed under the MIT license, of which you can find a copy here. The toolbox is ran by Vincent Lostanlen, a PhD student in the team of Stéphane Mallat at École normale supérieure in Paris. Ideas for academic collaboration are welcome.