Iterative Gaussianization: From ICA to Random Rotations

Abstract—Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this paper, 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 univariate marginal Gaussianization transform followed by an orthonormal 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. RBIG is formally similar to classical iterative projection pursuit algorithms. However, we show that, unlike in PP methods, the particular class of rotations 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 ...

• Type: Journal
• Year: 2011
• Where: TNN
• Authors: Valero Laparra, Gustavo Camps-Valls, Jesus Malo
• Keywords: Marginal Gaussianization, Rotation-based Iterative Gaussianization, TNN 2011, Univariate Marginal Gaussianization