### Abstract

Figures of merit for image quality are derived on the basis of the performance of mathematical observers on specific detection and estimation tasks. The tasks include detection of a known signal superimposed on a known background, detection of a known signal on a random background, estimation of Fourier coefficients of the object, and estimation of the integral of the object over a specified region of interest. The chosen observer for the detection tasks is the ideal linear discriminant, which we call the Hotelling observer. The figures of merit are based on the Fisher information matrix relevant to estimation of the Fourier coefficients and the closely related Fourier crosstalk matrix introduced earlier by Barrett and Gifford [Phys. Med. Biol. 39, 451 (1994)]. A finite submatrix of the infinite Fisher information matrix is used to set Cramer-Rao lower bounds on the variances of the estimates of the first N Fourier coefficients. The figures of merit for detection tasks are shown to be closely related to the concepts of noise-equivalent quanta (NEQ) and generalized NEQ, originally derived for linear, shift-invariant imaging systems and stationary noise. Application of these results to the design of imaging systems is discussed.

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

Pages (from-to) | 834-852 |

Number of pages | 19 |

Journal | Journal of the Optical Society of America. A, Optics and image science |

Volume | 12 |

Issue number | 5 |

State | Published - May 1995 |

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### ASJC Scopus subject areas

- Medicine(all)

### Cite this

*Journal of the Optical Society of America. A, Optics and image science*,

*12*(5), 834-852.

**Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance.** / Barrett, Harrison H; Denny, J. L.; Wagner, R. F.; Myers, K. J.

Research output: Contribution to journal › Article

*Journal of the Optical Society of America. A, Optics and image science*, vol. 12, no. 5, pp. 834-852.

}

TY - JOUR

T1 - Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance.

AU - Barrett, Harrison H

AU - Denny, J. L.

AU - Wagner, R. F.

AU - Myers, K. J.

PY - 1995/5

Y1 - 1995/5

N2 - Figures of merit for image quality are derived on the basis of the performance of mathematical observers on specific detection and estimation tasks. The tasks include detection of a known signal superimposed on a known background, detection of a known signal on a random background, estimation of Fourier coefficients of the object, and estimation of the integral of the object over a specified region of interest. The chosen observer for the detection tasks is the ideal linear discriminant, which we call the Hotelling observer. The figures of merit are based on the Fisher information matrix relevant to estimation of the Fourier coefficients and the closely related Fourier crosstalk matrix introduced earlier by Barrett and Gifford [Phys. Med. Biol. 39, 451 (1994)]. A finite submatrix of the infinite Fisher information matrix is used to set Cramer-Rao lower bounds on the variances of the estimates of the first N Fourier coefficients. The figures of merit for detection tasks are shown to be closely related to the concepts of noise-equivalent quanta (NEQ) and generalized NEQ, originally derived for linear, shift-invariant imaging systems and stationary noise. Application of these results to the design of imaging systems is discussed.

AB - Figures of merit for image quality are derived on the basis of the performance of mathematical observers on specific detection and estimation tasks. The tasks include detection of a known signal superimposed on a known background, detection of a known signal on a random background, estimation of Fourier coefficients of the object, and estimation of the integral of the object over a specified region of interest. The chosen observer for the detection tasks is the ideal linear discriminant, which we call the Hotelling observer. The figures of merit are based on the Fisher information matrix relevant to estimation of the Fourier coefficients and the closely related Fourier crosstalk matrix introduced earlier by Barrett and Gifford [Phys. Med. Biol. 39, 451 (1994)]. A finite submatrix of the infinite Fisher information matrix is used to set Cramer-Rao lower bounds on the variances of the estimates of the first N Fourier coefficients. The figures of merit for detection tasks are shown to be closely related to the concepts of noise-equivalent quanta (NEQ) and generalized NEQ, originally derived for linear, shift-invariant imaging systems and stationary noise. Application of these results to the design of imaging systems is discussed.

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UR - http://www.scopus.com/inward/citedby.url?scp=0029299915&partnerID=8YFLogxK

M3 - Article

C2 - 7730951

AN - SCOPUS:0029299915

VL - 12

SP - 834

EP - 852

JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision

JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision

SN - 1084-7529

IS - 5

ER -