Noise-Enhanced Information Systems

Abstract

Abstract-Noise, traditionally defined as an unwanted signal or disturbance, has been shown to play an important constructive role in many information processing systems and algorithms. This noise enhancement has been observed and employed in many physical, biological, and engineered systems. Indeed stochastic facilitation (SF) has been found critical for certain biological information functions like detection of weak, subthreshold stimuli or suprathreshold signals through both experimental verification and analytical model simulations.In this paper, we present a systematic noise-enhanced information processing framework to analyze and optimize the performance of engineered systems. System performance is evaluated not only in terms of signal-to-noise ratio but also in terms of other more relevant metrics such as probability of error for signal detection or mean square error for parameter estimation.As an important new instance of SF, we also discuss the constructive effect of noise in associative memory recall. Potential enhancement of image processing systems via the addition of noise is discussed with important applications in biomedical image enhancement, image denoising and classification.

Optimal Noise Benefit in Composite Hypothesis Testing under Different Criteria

“…From Figure 1, M is the minimum detection probability obtained by the noise enhanced Max-min approach. At the same time, M is the achievable maximum of the minimum detection probability in the three different noise-enhanced approaches, which is consistent with the definition given in Equation (13). Additionally, the value of M is independent of τ and With the decrease of τ , the maximum noise-modified average detection probability obtained by the restricted NP approach decreases, and the corresponding value of C increases and approaches M .…”

“…From Figure 1, M is the minimum detection probability obtained by the noise enhanced Max-min approach. At the same time, M is the achievable maximum of the minimum detection probability in the three different noise-enhanced approaches, which is consistent with the definition given in Equation (13). Additionally, the value of M is independent of τ and M = 0.8988.…”

“…The concept of SR was first brought up by Benzi et al in the process of exploring the periodic recurrence of ice gases [1] and since then the positive effects of noise have increasingly attracted researchers' attention in various fields, such as physics, chemistry, biology, and electronics [2][3][4][5][6][7][8][9]. The performance boost of a noise-enhanced system has also been observed in numerous signal detection problems; for example, when adjusting the background noise level or injecting additive noise to the input, the output of the system can be improved in some cases [10][11][12][13][14][15]. The improvements obtained via noise can be measured by various metrics, such as an increase in mutual information (MI) [16][17][18][19], output signal-to-noise ratio (SNR) [20][21][22], or detection probability [23][24][25][26][27][28][29], or a decrease in Bayes risk [30][31][32] or error probability [33].…”

Noise enhanced binary hypothesis-testing in a new framework

“…On the contrary, the positive effect of noise has been paid widespread concern by researchers since Benzi first proposed the concept of stochastic resonance (SR) [2][3][4][5][6][7][8][9]. Some of the more representative studies of SR in signal and information processing are shown as below: a nonlinear bistable autoregressive model applied in signal detection by S. Zozor [4,5], the noise enhanced detection performance under the Neyman-Pearson criterion analyzed by H. Chen [7,8], etc.…”

“…Such as, the noise enhanced performance of optimal Neyman-Pearson, Bayes and Minimax detectors are studied in [16], which proves that the performance of optimal detectors can be improved by increasing noise level of system under certain conditions. According to Neyman-Pearson criterion, the purpose is to increase the detection probability under the constraint on falsealarm probability [7,8,12]. In [7], a mathematical framework to analyze the noise enhanced effect in binary hypothesis testing problems is developed based on Neyman-Pearson criterion.…”