Quadratic tasks and the ideal observer

R. F. Wagner, H. H. Barrett

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The conventional whitening matched filter is linear in the data, even for edge-detection and object-location tasks. We have considered some special cases of the next order, or quadratic, matched filter which is second order in the data. Whereas integrals of NEQ-like quantities determine the performance of the linear filter, integrals of squared NEQ-like quantities determine the performance of the nonlinear filter. In the low contrast limit the NEQ-like quantities are precisely NEQ (noise equivalent quanta), and otherwise can be found by the Karhunen-Loeve transformation. The higher power means that these tasks are more sensitive to the higher frequency response of the hardware than are the linear tasks. Whether the human observer is capable of such quadratic tasks is an interesting open question.

Original languageEnglish (US)
Pages (from-to)306-309
Number of pages4
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - Jan 1 1987

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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