Post-nonlinear Blind Source Separation Research Articles

Sparsity enhancement post-nonlinear blind deconvolution method and its application to aluminum honeycomb panel cabin structure

In this paper, we propose a method for post-nonlinear blind source separation. The method divides the separation process of post-nonlinear mixed signals into two independent stages: the nonlinear compensation stage and the linear blind source separation stage. The nonlinear compensation stage is achieved by taking sparsity enhancement as the optimization objective. The L1-norm is taken as the objective function and is combined with the fast iteration based on the gradient descent method to realize the fast nonlinear compensation of the mixed signals. In the stage of linear blind source separation, the blind deconvolution algorithm with reference signals is used to process the compensated signals to realize the separation of the source signals. The separation performance of the method is verified by simulation, and the superiority of the method is tested by comparison. The proposed method is also investigated by the excitation experiment of the aluminum honeycomb panel cabin structure, which simulates the satellite structure.

Post-nonlinear blind source separation with kurtosis constraints using augmented Lagrangian particle swarm optimization and its application to mechanical systems

To accurately estimate source signals from their post-nonlinear mixtures, a post-nonlinear blind source separation (PNLBSS) method with kurtosis constraints is proposed based on augmented Lagrangian particle swarm optimization (PSO). First, an improved contrast function is presented by combining mutual information of the separated signals and kurtosis ranges of source signals. Second, an augmented Lagrangian multiplier method is used to convert PNLBSS into an unconstrained pseudo-objective optimization problem. Then, improved PSO is applied to update the parameters in complex nonlinear spaces. Finally, numerical case studies and experimental case studies are provided to evaluate the performance of the proposed method. By adding the kurtosis ranges constraints, the estimation accuracy of source signals could be improved, which would benefit vibration and acoustic monitoring and control.

EFFICIENT TECHNIQUE FOR BLIND SEPARATION OF POST-NONLINEAR MIXED SIGNALS

This paper proposes a new method to solve the post-nonlinear blind source separation problem (PNLBSS). The method is based on the fact that the distribution of the output signals of the linearly mixed system are approximately Gaussian distributed. According to the central limit theory, if one can manage the probability density function (PDF) of the nonlinear mixed signals to be Gaussian distribution, then this means that the signals becomes linearly mixed in spite of the PDF of its separate components. In this paper, the short time Gaussianization utilizing the B-spline neural network is used to ensure that the distribution of the signal is converted to the Gaussian distribution. These networks are built using neurons with flexible B-spline activation functions. The fourth order moment is used as a measurement of Gaussianization. After finishing the Gaussianization step, linear blind source separation method is used to recover the original signals. Performed computer simulations have shown the effectiveness of the idea, even in presence of strong nonlinearities and synthetic mixture of real world data.

MISEP Method for Postnonlinear Blind Source Separation

In this letter, a standard postnonlinear blind source separation algorithm is proposed, based on the MISEP method, which is widely used in linear and nonlinear independent component analysis. To best suit a wide class of postnonlinear mixtures, we adapt the MISEP method to incorporate a priori information of the mixtures. In particular, a group of three-layered perceptrons and a linear network are used as the unmixing system to separate sources in the postnonlinear mixtures, and another group of three-layered perceptron is used as the auxiliary network. The learning algorithm for the unmixing system is then obtained by maximizing the output entropy of the auxiliary network. The proposed method is applied to postnonlinear blind source separation of both simulation signals and real speech signals, and the experimental results demonstrate its effectiveness and efficiency in comparison with existing methods.

A spectral clustering approach to underdetermined postnonlinear blind source separation of sparse sources

This letter proposes a clustering-based approach for solving the underdetermined (i.e., fewer mixtures than sources) postnonlinear blind source separation (PNL BSS) problem when the sources are sparse. Although various algorithms exist for the underdetermined BSS problem for sparse sources, as well as for the PNL BSS problem with as many mixtures as sources, the nonlinear problem in an underdetermined scenario has not been satisfactorily solved yet. The method proposed in this letter aims at inverting the different nonlinearities, thus reducing the problem to linear underdetermined BSS. To this end, first a spectral clustering technique is applied that clusters the mixture samples into different sets corresponding to the different sources. Then, the inverse nonlinearities are estimated using a set of multilayer perceptrons (MLPs) that are trained by minimizing a specifically designed cost function. Finally, transforming each mixture by its corresponding inverse nonlinearity results in a linear underdetermined BSS problem, which can be solved using any of the existing methods.

Blind separation of post-nonlinear mixtures using linearizing transformations and temporal decorrelation

We propose two methods that reduce the post-nonlinear blind source separation problem (PNL-BSS) to a linear BSS problem. The first method is based on the concept of maximal correlation: we apply th...

Post-nonlinear blind source separation using methaheuristics

Genetic and gradient-based algorithms for post-nonlinear blind source separation are hybridised. Simulations show the effectiveness of the approach.

10.1162/jmlr.2003.4.7-8.1319

We propose two methods that reduce the post-nonlinear blind source separation problem (PNL-BSS) to a linear BSS problem. The first method is based on the concept of maximal correlation: we apply the alternating conditional expectation (ACE) algorithm---a powerful technique from non-parametric statistics---to approximately invert the componentwise non-linear functions.The second method is a Gaussianizing transformation, which is motivated by the fact that linearly mixed signals before nonlinear transformation are approximately Gaussian distributed. This heuristic, but simple and efficient procedure works as good as the ACE method.Using the framework provided by ACE, convergence can be proven. The optimal transformations obtained by ACE coincide with the sought-after inverse functions of the nonlinearities. After equalizing the nonlinearities, temporal decorrelation separation (TDSEP) allows us to recover the source signals. Numerical simulations testing ACE-TD and Gauss-TD on realistic examples are performed with excellent results.