1 January 1987 Quadratic Tasks And The Ideal Observer
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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.
© (1987) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
R. F. Wagner, R. F. Wagner, H. H. Barrett, H. H. Barrett, "Quadratic Tasks And The Ideal Observer", Proc. SPIE 0767, Medical Imaging, (1 January 1987); doi: 10.1117/12.967011; https://doi.org/10.1117/12.967011

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