Stochastic resonance as dithering

Wannamaker, Robert A.; Lipshitz, Stanley P.; Vanderkooy, John

doi:10.1103/physreve.61.233

Cited by 40 publications

(21 citation statements)

References 14 publications

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“…Too much noise swamps the image and degrades its contours. Gammaitoni [29] and others [70] have proposed a dithering argument for this SR effect and still others [55] have applied this argument to still images. The argument involves adding dither noise to a signal before quantization.…”

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confidence: 99%

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

Mitaim

Kosko

2004

IEEE Trans. Neural Netw.

105

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Abstract-Noise can improve how memoryless neurons process signals and maximize their throughput information. Such favorable use of noise is the so-called "stochastic resonance" or SR effect at the level of threshold neurons and continuous neurons. This paper presents theoretical and simulation evidence that 1) lone noisy threshold and continuous neurons exhibit the SR effect in terms of the mutual information between random input and output sequences, 2) a new statistically robust learning law can find this entropy-optimal noise level, and 3) the adaptive SR effect is robust against highly impulsive noise with infinite variance. Histograms estimate the relevant probability density functions at each learning iteration. A theorem shows that almost all noise probability density functions produce some SR effect in threshold neurons even if the noise is impulsive and has infinite variance. The optimal noise level in threshold neurons also behaves nonlinearly as the input signal amplitude increases. Simulations further show that the SR effect persists for several sigmoidal neurons and for Gaussian radial-basis-function neurons.Index Terms-Alpha-stable noise, impulsive noise, infinite-variance statistics, mutual information, noise processing, sigmoidal neurons and radial basis functions, stochastic gradient learning, stochastic resonance (SR), threshold neurons. I. NOISE AND ADAPTIVE STOCHASTIC RESONANCE NOISE is an unwanted signal or source of energy. Scientists and engineers have largely tried to filter noise or cancel it or mask it out of existence. The Noise Pollution Clearinghouse condemns noise outright: "Noise is unwanted sound. It is derived from the Latin word 'nausea' meaning seasickness. Noise is among the most pervasive pollutants today. Noise from road traffic, jet planes, jet skis, garbage trucks, construction equipment, manufacturing processes, lawn mowers, leaf blowers, and boom boxes, to name a few, are among the unwanted sounds that are routinely broadcast into the air."The Fig. 1 shows how uniform pixel noise can improve our subjective perception of an image. The system quantizes the original gray-scale "Lena" image into a binary image of black and white pixels. It emits a white pixel as output if the input gray-scale pixel equals or exceeds a threshold. It emits a black pixel as output if the input gray-scale pixel falls below the threshold. This quantizer is biased because it does not set the threshold at the midpoint of the gray scale. So the quantized version of the original image contains almost no information. A small level of noise sharpens the image contours and helps fill in features when it adds to the original image before the system applies the threshold. Too much noise swamps the image and degrades its contours. Gammaitoni [29] and others [70] have proposed a dithering argument for this SR effect and still others [55] have applied this argument to still images. The argument involves adding dither noise to a signal before quantization. Consider gray-scale pixel and binary output pixel wi...

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confidence: 99%

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

Mitaim

Kosko

2004

IEEE Trans. Neural Netw.

105

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“…Also, most reports on stochastic resonance with images have dealt with threshold or potential-barrier nonlinearities, where the noise essentially assists a small signal in overcoming a threshold or barrier. In this context of threshold nonlinearities, more specific techniques like dithering can be viewed as a special form of stochastic resonance [15]- [17]. Yet, stochastic resonance can occur in other types of nonlinearities, and we show it here with saturation as well as threshold nonlinearities.…”

Section: Introductionmentioning

confidence: 96%

Structural Similarity Measure to Assess Improvement by Noise in Nonlinear Image Transmission

Rousseau

Delahaies

Chapeau‐Blondeau

2010

IEEE Signal Process. Lett.

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We show that the structural similarity index is able to register stochastic resonance or improvement by noise in nonlinear image transmission, and sometimes when not registered by traditional measures of image similarity, and that in this task this index remains in good match with the visual appreciation of image quality.Index Terms-Image quality measure, improvement by noise, nonlinearity, stochastic resonance, structural similarity.

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“…Stochastic Resonance(SR) was first proposed as an explanation of the observed periodicity in the ice ages on earth [1][2][3][4],but has since been observed in a large variety of physical, chemical and biological systems [5].In recent years, the weak signal detection under the strong noise background through the stochastic resonance (SR) has been proposed as a useful means in a wide variety of systems [6][7][8][9][10][11][12][13],including bistable system [6,8,14,15],excitable systems [16],threshold systems [17][18][19][20][21],and biological systems [7,13].…”

Section: Introductionmentioning

confidence: 99%

A new piecewise-linear stochastic resonance model

Wang

Zhao

2009

2009 IEEE International Conference on Systems, Man and Cybernetics

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We put forward a new piecewise-linear stochastic resonance(SR) model for detecting the weak signal under the strong noise background for the large parameter case. Parameters of this piecewise-linear stochastic resonance system are less correlated than those of the traditional continuous nonlinear bistable system, so that it is much easier to adjust the response characteristic of this system and generate the SR under the large parameter signals case. Here we show its description equations and character parameters. Through numerically simulating its performance under the noiseless, noisy, small parameter and large parameter cases respectively, we illustrate that this system is very helpful for detecting the weak signal under the strong noise background not only for the small parameters case, but also for the large parameters case.

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Stochastic resonance as dithering

Cited by 40 publications

References 14 publications

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

Structural Similarity Measure to Assess Improvement by Noise in Nonlinear Image Transmission

A new piecewise-linear stochastic resonance model

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