## Source Separation Using Higher Order Moments (1989)

Venue: | in Proc. ICASSP |

Citations: | 94 - 7 self |

### BibTeX

@INPROCEEDINGS{Cardoso89sourceseparation,

author = {Jean-François Cardoso},

title = {Source Separation Using Higher Order Moments},

booktitle = {in Proc. ICASSP},

year = {1989},

pages = {2109--2112}

}

### Years of Citing Articles

### OpenURL

### Abstract

This communication presents a simple algebraic method for the extraction of independent components in multidimensional data. Since statistical independence is a much stronger property than uncorrelation, it is possible, using higher-order moments, to identify source signatures in array data without any a-priori model for propagation or reception, that is, without directional vector parametrization, provided that the emitting sources be independent with different probability distributions. We propose such a "blind" identification procedure. Source signatures are directly identified as covariance eigenvectors after data have been orthonormalized and non linearily weighted. Potential applications to Array Processing are illustrated by a simulation consisting in a simultaneous range-bearing estimation with a passive array. INTRODUCTION For a lot of reasons (of various kinds), the most common Signal Processing methods deal with second-order statistics, expressed in terms of covariance matr...

### Citations

494 |
Time Series: Data Analysis and Theory
- Brillinger
- 2001
(Show Context)
Citation Context ... statistics. Nonetheless, when the Gaussian assumption is not valid, some information is lost by retaining only second-order statistics. This information, which can be expressed in terms of cumulants =-=[1]-=-, is sometimes necessary, for instance in the problem of identifying a non-minimal phase process [2,3]. In the recent years, research on higher-order statistics has mainly focused on Time Series Analy... |

72 |
Bispectral estimation: A digital signal processing framework
- Nikias, Raghuveer
- 1987
(Show Context)
Citation Context ...g a non-minimal phase process [2,3]. In the recent years, research on higher-order statistics has mainly focused on Time Series Analysis, often using more specific description tools such as bispectra =-=[4,5]-=-. In contrast, less attention was given to applications in Multidimensional Signal Processing. In Array Processing, recently proposed methods for High Resolution are also based on structural analysis ... |

52 |
Détection de grandeurs primitives dans un message composite par une architecture de calcul neuromimétique en apprentissage non supervise
- Hérault, Jutten, et al.
- 1985
(Show Context)
Citation Context ...f blind separation of multidimensional components by taking advantage of statistical independence has already been adressed in recent litterature. A non-linear adaptive procedure has been proposed in =-=[9,10]-=- while a direct solution using explicitely cumulants was given for the case of two sources and two sensors in [11]. In contrast, we propose here a simple algebraic method to separate an arbitrary numb... |

22 |
Identification of linear stochastic systems via second order and fourth-order cumulant matching
- Tugnait
- 1987
(Show Context)
Citation Context ...aining only second-order statistics. This information, which can be expressed in terms of cumulants [1], is sometimes necessary, for instance in the problem of identifying a non-minimal phase process =-=[2,3]-=-. In the recent years, research on higher-order statistics has mainly focused on Time Series Analysis, often using more specific description tools such as bispectra [4,5]. In contrast, less attention ... |

13 |
Triple correlations
- Lohmann, Wirnitzer
- 1984
(Show Context)
Citation Context ...g a non-minimal phase process [2,3]. In the recent years, research on higher-order statistics has mainly focused on Time Series Analysis, often using more specific description tools such as bispectra =-=[4,5]-=-. In contrast, less attention was given to applications in Multidimensional Signal Processing. In Array Processing, recently proposed methods for High Resolution are also based on structural analysis ... |

12 |
Sources identification : a solution based on the cumulants
- Lacoume, Ruiz
- 1988
(Show Context)
Citation Context ...dressed in recent litterature. A non-linear adaptive procedure has been proposed in [9,10] while a direct solution using explicitely cumulants was given for the case of two sources and two sensors in =-=[11]-=-. In contrast, we propose here a simple algebraic method to separate an arbitrary number of sources, given measurements from a larger number of sensors. THE SOURCE SEPARATION PROBLEM We are given an a... |

11 |
Cumulant-Based Approach to the Harmonic Retrieval and Related Problems
- SWAMI
- 1991
(Show Context)
Citation Context ... as a consequence, the problem of source location is analog to a harmonic retrieval problem. Most of the work on using higher order information in Array Processing has been done within this framework =-=[6,7,8]-=-. However, actual physical settings are often such that source signatures (directional vectors) depart from the assumed model. As expected, model-based methods are very sensitive to such discrepancies... |

10 |
Component Analysis versus Principal Components Analysis,” presented at
- Jutten, Herault
- 1988
(Show Context)
Citation Context ...f blind separation of multidimensional components by taking advantage of statistical independence has already been adressed in recent litterature. A non-linear adaptive procedure has been proposed in =-=[9,10]-=- while a direct solution using explicitely cumulants was given for the case of two sources and two sensors in [11]. In contrast, we propose here a simple algebraic method to separate an arbitrary numb... |

5 |
G.Ruget, "Robust Identification of a Nonminimum Phase System: Blind Adjustement of a Linear Equalizer
- Benveniste, Goursat
- 1980
(Show Context)
Citation Context ...aining only second-order statistics. This information, which can be expressed in terms of cumulants [1], is sometimes necessary, for instance in the problem of identifying a non-minimal phase process =-=[2,3]-=-. In the recent years, research on higher-order statistics has mainly focused on Time Series Analysis, often using more specific description tools such as bispectra [4,5]. In contrast, less attention ... |

5 |
Harmonic Decomposition Methods in Cumulant Domains
- Pan, Nikias
- 1988
(Show Context)
Citation Context ... as a consequence, the problem of source location is analog to a harmonic retrieval problem. Most of the work on using higher order information in Array Processing has been done within this framework =-=[6,7,8]-=-. However, actual physical settings are often such that source signatures (directional vectors) depart from the assumed model. As expected, model-based methods are very sensitive to such discrepancies... |

2 |
On the Use of Higher Order Information
- Amengual, Vallverdu, et al.
- 1988
(Show Context)
Citation Context ... as a consequence, the problem of source location is analog to a harmonic retrieval problem. Most of the work on using higher order information in Array Processing has been done within this framework =-=[6,7,8]-=-. However, actual physical settings are often such that source signatures (directional vectors) depart from the assumed model. As expected, model-based methods are very sensitive to such discrepancies... |

2 |
Multiple Emitter Loaction and Signal Parameter Estimation
- Schmidt
- 1979
(Show Context)
Citation Context ...ecessarily different. Nonetheless we show here simulations intended to demonstrate its ability to deal with source location problems. We run, on the same set set of data, FOBI and the MUSIC algorithm =-=[12]-=-. We consider a passive listening linear array of 8 identical sensors. Distance between sensors is 1 m and wavelength is 2 m. Two sources are present: the first one is Gaussian, located 100 m away fro... |