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Applied Optics

Applied Optics


  • Vol. 36, Iss. 32 — Nov. 10, 1997
  • pp: 8352–8357

Invariant error metrics for image reconstruction

J. R. Fienup  »View Author Affiliations

Applied Optics, Vol. 36, Issue 32, pp. 8352-8357 (1997)

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Expressions are derived for the normalized root-mean-square error of an image relative to a reference image. Different versions of the error metric are invariant to different combinations of effects, including the image’s (a) being multiplied by a real or complex-valued constant, (b) having a constant added to its phase, (c) being translated, or (d) being complex conjugated and rotated 180°. Invariance to these effects is particularly important for the phase-retrieval problem. One can also estimate the parameters of those effects. Similarly, two wave fronts can be compared, allowing for arbitrary constant (piston) and linear (tilt) phase terms. One can also include a weighting function. The relation between the error metric and other quality measures is derived.

© 1997 Optical Society of America

Original Manuscript: May 5, 1997
Published: November 10, 1997

J. R. Fienup, "Invariant error metrics for image reconstruction," Appl. Opt. 36, 8352-8357 (1997)

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  1. E. H. Linfoot, Fourier Methods in Optical Image Evaluation (The Focal Press, London, 1964).
  2. A. Eskicioglu, P. S. Fisher, “Image quality measures and their performance,” IEEE Trans. Commun. 12, 2959–2965 (1995). [CrossRef]
  3. J. R. Fienup, A. M. Kowalczyk, “Phase retrieval for a complex-valued object by using a low-resolution image,” J. Opt. Soc. Am. A 7, 450–458 (1990). [CrossRef]
  4. M. Born, E. Wolf, Progress in Optics (MacMillan, New York, 1964), Sec. 9.1.3.

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