Separation of Nonlinear Image Mixtures by Denoising Source Separation

Almeida, Mariana S. C.; Valpola, Harri; Särelä, Jaakko

doi:10.1007/11679363_2

Cited by 11 publications

(15 citation statements)

References 4 publications

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“…The method provides good separation results in several low-dimensional artificial examples as well as in a real nonlinear image mixture problem [23], but it has not been demonstrated for more than 4 mixtures of 4 sources. Nonlinear denoising source separation [24] can also be applied to separate low-dimensional nonlinear mixtures.…”

Section: Existing Methodsmentioning

confidence: 99%

Blind separation of nonlinear mixtures by variational Bayesian learning

Honkela¹,

Valpola²,

Ilin³

et al. 2007

Digital Signal Processing

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Blind separation of sources from nonlinear mixtures is a challenging and often illposed problem. We present three methods for solving this problem: an improved nonlinear factor analysis (NFA) method using multilayer perceptron (MLP) network to model the nonlinearity, a hierarchical NFA (HNFA) method suitable for larger problems and a post-nonlinear NFA (PNFA) method for more restricted post-nonlinear mixtures. The methods are based on variational Bayesian learning, which provides the needed regularisation and allows for easy handling of missing data. While the basic methods are incapable of recovering the correct rotation of the source space, they can discover the underlying nonlinear manifold and allow reconstruction of the original sources using standard linear independent component analysis (ICA) techniques.

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Section: Existing Methodsmentioning

confidence: 99%

Blind separation of nonlinear mixtures by variational Bayesian learning

Honkela¹,

Valpola²,

Ilin³

et al. 2007

Digital Signal Processing

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“…12 The fact that the sources can be recovered up to permutation, scaling, and translation implies that each g i must be the inverse of the corresponding f i , up to unknown translation and scaling, and thus that the nonlinearities of the mixture can be estimated, up to unknown translations and scalings. The need for the first condition (that A must have at least two nonzero elements per row and/or per column) can be understood in the following way: If A had just one nonzero element per row and per column, it would correspond just to a permutation and a scaling.…”

Section: Post-nonlinear Mixturesmentioning

confidence: 99%

Nonlinear Source Separation

Almeida¹

2006

Synthesis Lectures on Signal Processing

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The purpose of this lecture book is to present the state of the art in nonlinear blind source separation, in a form appropriate for students, researchers and developers. Source separation deals with the problem of recovering sources that are observed in a mixed condition. When we have little knowledge about the sources and about the mixture process, we speak of blind source separation. Linear blind source separation is a relatively well studied subject. Nonlinear blind source separation is still in a less advanced stage, but has seen several significant developments in the last few years.This publication reviews the main nonlinear separation methods, including the separation of post-nonlinear mixtures, and the MISEP, ensemble learning and kTDSEP methods for generic mixtures. These methods are studied with a significant depth. A historical overview is also presented, mentioning most of the relevant results, on nonlinear blind source separation, that have been presented over the years.

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“…In the most of ICA methods the result are achieved from adaptive or iterative algorithms which are time consuming procedures. Another work was based on the nonlinear denoising source separation (DSS) method [3]. This method suppose that two images have independent sources and have different frequency components in the same locations.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, nonlinear denoising might be used for source separation. The separation method used here is similar to that implemented in [3]. However, authors believe that human visual perception uses different edge directions in the mixed subjects two separate them.…”

Section: Introductionmentioning

confidence: 99%