Rotation-based Iterative Gaussianization [RBIG]

Code and results for the paper

"Iterative Gaussianization: from ICA to Random Rotations"
V. Laparra, G. Camps and J. Malo
IEEE Transactions on Neural Networks, 2010

Abstract

Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this work, we propose a solution to this problem by using a family of Rotation-based Iterative Gaussianization (RBIG) transforms. The general framework consists of the sequential application of a two-step
processing unit: univariate marginal Gaussianization transform followed by an orthogonal transform. The proposed procedure looks for differentiable transforms to a known PDF so that the unknown PDF can be estimated at any point of the original domain. In particular, we aim at a zero mean unit covariance Gaussian for convenience, but other distributions could be equally considered.

RBIG is formally similar to classical iterative Projection Pursuit (PP) algorithms. However, we show that, unlike in PP methods, the particular class of rotation used has no special qualitative relevance in this context, since looking for "interestingness" is not a critical issue for PDF estimation. The key difference is that our approach focuses on the univariate part of the problem rather than on the multivariate part which is related to interesting projections. This difference implies that one may select the most convenient rotation suited to each practical application.

The differentiability, invertibility and convergence of RBIG are theoretically and experimentally analyzed. Relation to other methods, such as Radial Gaussianization (RG), one-class support vector domain description (SVDD), and deep neural networks (DNN) is also pointed out. The practical performance of RBIG is successfully illustrated in a number of multidimensional problems such as image synthesis, classification, denoising, and multi-information estimation.

Download

Software: RBIG_toolbox.zip

Help on Software

• The provided software is an implementation of the proposed RBIG approach.

• See the file “using_RBIG_example.m” included in the *.zip file for details

References

FastICA Algorithm: http://www.cis.hut.fi/projects/ica/fastica/code/FastICA_2.5.zip

Copyright & Disclaimer

The programs are granted free of charge for research and education purposes only. Scientific results produced using the software provided shall acknowledge the use of the RBIG implementation provided by us. If you plan to use it for non-scientific purposes, don't hesitate to contact us.

Because the programs are licensed free of charge, there is no warranty for the program, to the extent permitted by applicable law. except when otherwise stated in writing the copyright holders and/or other parties provide the program "as is" without warranty of any kind, either expressed or implied, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. the entire risk as to the quality and performance of the program is with you. should the program prove defective, you assume the cost of all necessary servicing, repair or correction.

In no event unless required by applicable law or agreed to in writing will any copyright holder, or any other party who may modify and/or redistribute the program, be liable to you for damages, including any general, special, incidental or consequential damages arising out of the use or inability to use the program (including but not limited to loss of data or data being rendered inaccurate or losses sustained by you or third parties or a failure of the program to operate with any other programs), even if such holder or other party has been advised of the possibility of such damages.