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William H McIlhagga; Are human observers performing wavelet denoising?. Journal of Vision 2003;3(9):361. doi: https://doi.org/10.1167/3.9.361.
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Wavelet denoising (Donoho & Johnstone 1994) is a powerful method for removing noise from signals encoded by a set of wavelet coefficients. Many aspects of human detection and discrimination can be explained by assuming that the human visual system uses wavelet denoising in visual decision tasks.
In wavelet denoising, coefficients less than a threshold sigma*sqrt(2log(n)) are assumed to be mostly noise, and set to zero (sigma is the noise standard deviation and n is the number of coefficients). Applying this procedure to vision, an image is represented as the outputs of a set of n V1 neurons, which may form a sparse wavelet-like code (Field 1994). V1 neurons with activity less than the threshold are ignored in decision-making.
The denoising threshold is identical to the decision threshold implied by Pelli's (1985) uncertain observer. In Pelli's model, the observer is correct when one relevant detector exceeds the maximum of M irrelevant detectors, having expectation sigma*sqrt(2log(M)) (Galambos, 1985). Simulations of the denoising model show that it matches Pelli's model.
However, the denoising model can be extended in two ways. First, the noise threshold can be adapted to the frequency spectrum of the noise. Thus noise that differs substantially from the signal has little effect on detection. Second, the denoising model can be combined with template-based detection models, and this leads to a separation of intrinsic uncertainty (manifest through the denoising threshold) and extrinsic uncertainty (manifest through the use of multiple templates).
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PelliD.G.(1985) Uncertainty explains many aspects of visual contrast detection and discrimination, JOSA A2 1508–1532
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