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

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.

[1]  H H Barrett,et al.  Cone-beam tomography with discrete data sets. , 1994, Physics in medicine and biology.

[2]  R. F. Wagner,et al.  SNR and noise measurements for medical imaging: I. A practical approach based on statistical decision theory. , 1993, Physics in medicine and biology.

[3]  Gabor T. Herman,et al.  Evaluators of image reconstruction algorithms , 1989, Int. J. Imaging Syst. Technol..

[4]  G. Backus,et al.  Numerical Applications of a Formalism for Geophysical Inverse Problems , 1967 .

[5]  Harrison H. Barrett,et al.  III The Radon Transform and Its Applications , 1984 .

[6]  R. F. Wagner,et al.  Aperture optimization for emission imaging: effect of a spatially varying background. , 1990, Journal of the Optical Society of America. A, Optics and image science.

[7]  B. Tsui,et al.  Noise properties of the EM algorithm: II. Monte Carlo simulations. , 1994, Physics in medicine and biology.

[8]  Richard Greenwood Paxman.  COORDINATED DESIGN OF RESTORATION ALGORITHM AND CODED APERTURE (RECONSTRUCTION, TOMOGRAPHY). , 1984 .

[9]  A O Hero,et al.  Information analysis of single photon emission computed tomography with count losses. , 1990, IEEE transactions on medical imaging.

[10]  G T Herman,et al.  Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography. , 1991, IEEE transactions on medical imaging.

[11]  Alfred O. Hero,et al.  A fast recursive algorithm for computing CR-type bounds for image reconstruction problems , 1992, IEEE Conference on Nuclear Science Symposium and Medical Imaging.

[12]  H H Barrett,et al.  Objective assessment of image quality: effects of quantum noise and object variability. , 1990, Journal of the Optical Society of America. A, Optics and image science.

[13]  Mario Bertero,et al.  Linear inverse problems with discrete data. I. General formulation and singular system analysis , 1985 .

[14]  R. F. Wagner,et al.  Unified SNR analysis of medical imaging systems , 1985, Physics in medicine and biology.

[15]  H H Barrett,et al.  Addition of a channel mechanism to the ideal-observer model. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[16]  Stefan P. Mueller,et al.  Barankin bound: a model of detection with location uncertainty , 1992, Optics & Photonics.

[17]  Charles R. Johnson,et al.  Topics in matrix analysis: The Hadamard product , 1991 .

[18]  H H Barrett,et al.  Hotelling trace criterion and its correlation with human-observer performance. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[19]  Jannick P. Rolland,et al.  Linear discriminants and image quality , 1991, Image Vis. Comput..

[20]  H H Barrett,et al.  Effect of random background inhomogeneity on observer detection performance. , 1992, Journal of the Optical Society of America. A, Optics and image science.

[21]  R. Shaw,et al.  The Equivalent Quantum Efficiency of the Photographic Process , 1963 .

[22]  Jie Yao,et al.  Predicting human performance by a channelized Hotelling observer model , 1992, Optics & Photonics.

[23]  Harrison H. Barrett,et al.  Hotelling trace criterion as a figure of merit for the optimization of imaging systems , 1986 .

[24]  Kyle J. Myers,et al.  Model observers for assessment of image quality , 1993 .

[25]  Charles E. Metz,et al.  On The Multiplex Advantage Of Coded Source/Aperture Photon Imaging , 1981, Other Conferences.

[26]  Jannick P. Rolland,et al.  Factors influencing lesion detection in medical imaging. , 1990 .

[27]  C. Metz.  ROC Methodology in Radiologic Imaging , 1986, Investigative radiology.

[28]  R. Shaw,et al.  Evaluating the efficient of imaging processes , 1978 .

[29]  C E Metz,et al.  A comparison of optimum detector spatial resolution in nuclear imaging based on statistical theory and on observer performance. , 1978, Physics in medicine and biology.

[30]  H.H. Barrett,et al.  Predicting the performance of gamma-ray imaging devices in the task of tumor detection , 1991, Conference Record of the 1991 IEEE Nuclear Science Symposium and Medical Imaging Conference.

[31]  M F Kijewski,et al.  Maximum-likelihood estimation: a mathematical model for quantitation in nuclear medicine. , 1990, Journal of nuclear medicine : official publication, Society of Nuclear Medicine.

[32]  H. Barrett,et al.  Effect of noise correlation on detectability of disk signals in medical imaging. , 1985, Journal of the Optical Society of America. A, Optics and image science.

[33]  Kenneth M. Hanson,et al.  Optimization for Object Localization of the Constrained Algebraic Reconstruction Technique , 1989, Medical Imaging.

[34]  Kenneth M. Hanson,et al.  Variations In Task And The Ideal Observer , 1983, Other Conferences.

[35]  Kyle J. Myers,et al.  Human and quasi-Bayesian observers of images limited by quantum noise, object-variability, and artifacts , 1994, Medical Imaging.

[36]  J A Swets,et al.  Measuring the accuracy of diagnostic systems. , 1988, Science.

[37]  Donald W. Wilson,et al.  Noise properties of the EM algorithm. I. Theory , 1994 .

[38]  R. F. Wagner,et al.  Efficiency of human visual signal discrimination. , 1981, Science.

[39]  H H Barrett,et al.  Image reconstruction from coded data: II. Code design. , 1985, Journal of the Optical Society of America. A, Optics and image science.