### Abstract

It is shown that a useful generalized linear filter W can be constructed from experimental data. The data are divided into many experiments and this ensemble is used to calculate the autocorrelation functions which appear in W. In turn, from this filter one determines a "Hamiltonian" ℋ. The eigenvectors and eigenvalues of this Hamiltonian are evaluated. For a "good" experiment there is one small eigenvalue, and the rest are ≈1. The W so determined usefully reduces the noise in a new data set. The presence of two or more small eigenvalues indicates that the experimental data contains more than a single signal. The action of W on selected members of the ensemble, and/or new data sets, extracts the different signals with, again, a useful noise reduction. Both computer simulations and real positron annihilation data are used to illustrate these development.

Original language | English (US) |
---|---|

Pages (from-to) | 679-701 |

Number of pages | 23 |

Journal | Journal of Statistical Physics |

Volume | 76 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 1994 |

### Fingerprint

### Keywords

- data analysis
- Generalized linear filters
- image processing

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*76*(1-2), 679-701. https://doi.org/10.1007/BF02188681

**Application of generalized linear filters in data analysis.** / Barnes, Stewart; Peter, M.; Hoffmann, L.; Manuel, A. A.; Shukla, A.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 76, no. 1-2, pp. 679-701. https://doi.org/10.1007/BF02188681

}

TY - JOUR

T1 - Application of generalized linear filters in data analysis

AU - Barnes, Stewart

AU - Peter, M.

AU - Hoffmann, L.

AU - Manuel, A. A.

AU - Shukla, A.

PY - 1994/7

Y1 - 1994/7

N2 - It is shown that a useful generalized linear filter W can be constructed from experimental data. The data are divided into many experiments and this ensemble is used to calculate the autocorrelation functions which appear in W. In turn, from this filter one determines a "Hamiltonian" ℋ. The eigenvectors and eigenvalues of this Hamiltonian are evaluated. For a "good" experiment there is one small eigenvalue, and the rest are ≈1. The W so determined usefully reduces the noise in a new data set. The presence of two or more small eigenvalues indicates that the experimental data contains more than a single signal. The action of W on selected members of the ensemble, and/or new data sets, extracts the different signals with, again, a useful noise reduction. Both computer simulations and real positron annihilation data are used to illustrate these development.

AB - It is shown that a useful generalized linear filter W can be constructed from experimental data. The data are divided into many experiments and this ensemble is used to calculate the autocorrelation functions which appear in W. In turn, from this filter one determines a "Hamiltonian" ℋ. The eigenvectors and eigenvalues of this Hamiltonian are evaluated. For a "good" experiment there is one small eigenvalue, and the rest are ≈1. The W so determined usefully reduces the noise in a new data set. The presence of two or more small eigenvalues indicates that the experimental data contains more than a single signal. The action of W on selected members of the ensemble, and/or new data sets, extracts the different signals with, again, a useful noise reduction. Both computer simulations and real positron annihilation data are used to illustrate these development.

KW - data analysis

KW - Generalized linear filters

KW - image processing

UR - http://www.scopus.com/inward/record.url?scp=34249765064&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249765064&partnerID=8YFLogxK

U2 - 10.1007/BF02188681

DO - 10.1007/BF02188681

M3 - Article

AN - SCOPUS:34249765064

VL - 76

SP - 679

EP - 701

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -