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We consider the nonlinear bistable dynamic system that is the archetypal system giving way to the phenomenon of stochastic resonance for noise-improved signal processing. Independently of a strict stochastic resonance effect, we use this bistable system as a nonlinear filter for a detection task on a binary signal. We expose a methodology to tune the nonlinear filter at its best performance that minimizes its probability of detection error. The optimally tuned nonlinear filter is then compared to the ideal matched filter, which is the optimal filter for the detection with Gaussian noise. We show that the performance of the nonlinear filter, although (expectedly) not as good, comes close to that of the ideal matched filter operating in its strict nominal conditions. We next examine several possible departures, quite plausible in practical operation, from the nominal conditions of the ideal matched filter. We demonstrate that in such degraded conditions, the nonlinear filter can catch up and surpass the performance of the matched filter. This reveals a robustness superiority of the nonlinear filter, compared to the matched filter operating outside its strict nominal conditions.

We review simple connectionist and firing rate models for mutually inhibiting pools of neurons that discriminate between pairs of stimuli. Both are two-dimensional nonlinear stochastic ordinary differential equations, and although they differ in how inputs and stimuli enter, we show that they are equivalent under state variable and parameter coordinate changes. A key parameter is gain: the maximum slope of the sigmoidal activation function. We develop piecewise-linear and purely linear models, and one-dimensional reductions to Ornstein–Uhlenbeck processes that can be viewed as linear filters, and show that reaction time and error rate statistics are well approximated by these simpler models. We then pose and solve the optimal gain problem for the Ornstein–Uhlenbeck processes, finding explicit gain schedules that minimize error rates for time-varying stimuli. We relate these to time courses of norepinephrine release in cortical areas, and argue that transient firing rate changes in the brainstem nucleus locus coeruleus may be responsible for approximate gain optimization.

This paper presents a thorough evaluation of a bistable system versus a matched filter in detecting bipolar pulse signals. The detectability of the bistable system can be optimized by adding noise, i.e. the stochastic resonance (SR) phenomenon. This SR effect is also demonstrated by approximate statistical detection theory of the bistable system and corresponding numerical simulations. Furthermore, the performance comparison results between the bistable system and the matched filter show that (a) the bistable system is more robust than the matched filter in detecting signals with disturbed pulse rates, and (b) the bistable system approaches the performance of the matched filter in detecting unknown arrival times of received signals, with an especially better computational efficiency. These significant results verify the potential applicability of the bistable system in signal detection field.

Recently, it was reported that some saturation nonlinearities could effectively act as noise-aided signal-noise-ratio amplifiers. In the letter we consider the signal detection performance of saturation nonlinearities driven by a sinusoidal signal buried in Gaussian white noise. It is showed that the signal detection statistics still undergo a nonmonotonic evolution as noise is raised. We also particularly show that an improvement of the SNR in terms of the first harmonic does not imply the possibility to improve the signal detection performance through stochastic resonance. The study might also complement other reports about stochastic resonance in saturation nonlinearities.

In this paper, we report that for a weak signal buried in the heavy-tailed noise, the bistable system can outperform the matched filter, yielding a higher output signal-to-noise ratio (SNR) or a lower probability of error. Moreover, by adding mutually independent internal noise components to an array of bistable systems, the output SNR or the probability of error can be further improved via the mechanism of stochastic resonance (SR). These comparison results demonstrate the potential capability of bistable systems for detecting weak signals in non-Gaussian noise environments.

An efficient and robust method for identification of coronary arteries and evaluation of the severity of the stenosis on the routine X-ray angiograms is proposed. It is a challenging process to accurately identify coronary artery due to poor signal-to-noise ratio, vessel overlap, and superimposition with various anatomical structures such as ribs, spine, or heart chambers. The proposed method consists of two major stages: (a) signal-based image segmentation and (b) vessel feature extraction. The 3D Fourier and 3D Wavelet transforms are first employed to reduce the background and noisy structures in the images. Afterwards, a set of matched filters was applied to enhance the coronary arteries in the images. At the end, clustering analysis, histogram technique, and size filtering were utilized to obtain a binary image that consists of the final segmented coronary arterial tree. To extract vessel features in terms of vessel centerline and diameter, a gradient vector-flow based snake algorithm is applied to determine the medial axis of a vessel followed by the calculations of vessel boundaries and width associated with the detected medial axis.

Locating the Optic Disc (OD) and Macula Center (MC) is the main step in the automatic extraction of retinal anatomical structures for Diabetic Retinopathy (DR). In this work, a variety of vessel segmentation methods have been adopted for the identification of OD in retinal images. In order to locate OD, different segmentation algorithms like matched filter, spatially weighed Fuzzy C-means and threshold are used to detect the blood vessels from the retinal image. Matching the expected directional pattern of the retinal blood vessels is proposed to locate the OD center. The proposed vessel direction filter is resized and OD center is measured. Macula center (fovea) is located at a constant distance from optic disc. A new method with geometric approach is proposed for macula detection. The proposed methods have been evaluated using a STARE and DRIVE datasets which contains both normal and diseased retina. The proposed methods are successfully adopted for segmentation of blood vessels and location of OD and MC in both normal and abnormal images.

We review simple connectionist and firing rate models for mutually inhibiting pools of neurons that discriminate between pairs of stimuli. Both are two-dimensional nonlinear stochastic ordinary differential equations, and although they differ in how inputs and stimuli enter, we show that they are equivalent under state variable and parameter coordinate changes. A key parameter is gain: the maximum slope of the sigmoidal activation function. We develop piecewise-linear and purely linear models, and one-dimensional reductions to Ornstein–Uhlenbeck processes that can be viewed as linear filters, and show that reaction time and error rate statistics are well approximated by these simpler models. We then pose and solve the optimal gain problem for the Ornstein–Uhlenbeck processes, finding explicit gain schedules that minimize error rates for time-varying stimuli. We relate these to time courses of norepinephrine release in cortical areas, and argue that transient firing rate changes in the brainstem nucleus locus coeruleus may be responsible for approximate gain optimization.