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A physical statistics theory for detectability of target signals in noisy images. I. Mathematical background, empirical review, and development of theory

Moran, P.R.

Medical Physics 9(3): 401-413

1982

This paper addresses the physical probability of finding, by random chance of noise fluctuations, false-positive events in the background field of view of a noisy image. The signal levels of these random events are characterized by a general noise power spectrum; if they are comparable in magnitude with that of a true target signal, averaged over an area equal to that of the true target signal, then the false-positive events obscure the confidence of the true signal identification. The theory shows that the statistics of this phenomenon depend very strongly, and with distinct threshold behavior, upon the generalized power-signal-to-noise ratio of the true target signal; the behavior depends only weakly upon other factors, e.g., the background field of view area examined with respect to the true target area. Evaluation of even the simplest model of detection confidence, based upon this theory, yields several immediate results. The predicted SNR at threshold is approximately 3.5, with a variation of +/- 0.5 from 10%-95% confidence-of-detection levels. The theory is applied also to systems where display or intrinsic signal detection properties, rather than system inputs, limit the statistics. In this case, the theory predicts, in agreement with experiments, contrast-limiting effects of 1% contrast for the human eye vision system and 5% contrast for typical TV displays of scintigraphic images. When experimental detectability studies of numerous investigators all are converted to a uniform specification of the output power-average-signal-to-noise ratio, then the theoretical predictions here give an excellent description of all major aspects of the empirical results.

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