Objective assessment of image quality. Ii. fisher information, fourier crosstalk, and figures of merit for task performance

Harrison H. Barrett, J. L. Denny, Robert F. Wagner, Kyle J. Myers

Research output: Contribution to journalArticle

190 Scopus citations

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 languageEnglish (US)
Pages (from-to)834-852
Number of pages19
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Volume12
Issue number5
DOIs
StatePublished - May 1995

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition

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