Name
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 the univariate part (marginal Gaussianization) of the problem rather than on the multivariate part (rotation). 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, one-class support vector domain description, and deep neural networks 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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/TNN.2011.2106511 | IEEE Transactions on Neural Networks |
Keywords | Field | DocType |
multidimensional probability density function,radial gaussianization,marginal gaussianization,convenient rotation,unknown pdf,random rotations,classical iterative projection pursuit,key difference,multi-information estimation,iterative gaussianization,univariate marginal gaussianization,pdf estimation,signal processing,neural network,wavelet analysis,rotation,computer simulation,iterative methods,probability density,algorithms,convergence,principal component analysis,normal distribution,estimation,independent component analysis,redundancy,negentropy,neural nets,projection pursuit,gaussian processes,image classification,probability density function,support vector machines | Density estimation,Projection pursuit,Computer science,Gaussian process,Artificial intelligence,Mathematical optimization,Pattern recognition,Iterative method,Algorithm,Orthonormal basis,Independent component analysis,Univariate,Probability density function | Journal |
Volume | Issue | ISSN |
22 | 4 | 1941-0093 |
Citations | PageRank | References |
24 | 1.03 | 28 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Valero Laparra | 1 | 143 | 17.34 |
| Camps-Valls, G. | 2 | 441 | 29.69 |
| J Malo | 3 | 195 | 32.92 |