Papers by François Chapeau-Blondeau
Capacity of very noisy communication channels based on Fisher information
Scientific reports, Jan 16, 2016
We generalize the asymptotic capacity expression for very noisy communication channels to now inc... more We generalize the asymptotic capacity expression for very noisy communication channels to now include coloured noise. For the practical scenario of a non-optimal receiver, we consider the common case of a correlation receiver. Due to the central limit theorem and the cumulative characteristic of a correlation receiver, we model this channel noise as additive Gaussian noise. Then, the channel capacity proves to be directly related to the Fisher information of the noise distribution and the weak signal energy. The conditions for occurrence of a noise-enhanced capacity effect are discussed, and the capacity difference between this noisy communication channel and other nonlinear channels is clarified.
In this paper, we investigate the first exploitation of the vibrational resonance (VR) effect to ... more In this paper, we investigate the first exploitation of the vibrational resonance (VR) effect to detect weak signals in the presence of strong background noise. By injecting a series of sinusoidal interference signals of the same amplitude but with different frequencies into a generalized correlation detector, we show that the detection probability can be maximized at an appropriate interference amplitude. Based on a dual-Dirac probability density model, we compare the VR method with the stochastic resonance approach via adding dichotomous noise. The compared results indicate that the VR method can achieve a higher detection probability for a wider variety of noise distributions.
We generalize the asymptotic capacity expression for very noisy communication channels to now inc... more We generalize the asymptotic capacity expression for very noisy communication channels to now include coloured noise. For the practical scenario of a non-optimal receiver, we consider the common case of a correlation receiver. Due to the central limit theorem and the cumulative characteristic of a correlation receiver, we model this channel noise as additive Gaussian noise. Then, the channel capacity proves to be directly related to the Fisher information of the noise distribution and the weak signal energy. The conditions for occurrence of a noise-enhanced capacity effect are discussed, and the capacity difference between this noisy communication channel and other nonlinear channels is clarified.
The Allison mixture is a random process formed by stochastically switching between two random and... more The Allison mixture is a random process formed by stochastically switching between two random and uncorrelated input processes. Unintuitively, these samples—independent prior to being drawn—can acquire dependence as a result of the sampling process. It has previously been shown that correlation can occur subject to certain conditions, however in general dependence does not imply correlation. In this paper we provide an initial information-theoretic analysis of the Allison mixture, and derive the autoinformation function of its sampling process as the first step towards a fuller information-theoretic analysis of its output.
Is it possible for a large sequence of measurements or observations, which support a hypothesis, ... more Is it possible for a large sequence of measurements or observations, which support a hypothesis, to counterintuitively decrease our confidence? Can unanimous support be too good to be true? The assumption of independence is often made in good faith; however, rarely is consideration given to whether a systemic failure has occurred. Taking this into account can cause certainty in a hypothesis to decrease as the evidence for it becomes apparently stronger. We perform a probabilistic Bayesian analysis of this effect with examples based on (i) archaeological evidence, (ii) weighing of legal evidence and (iii) cryptographic primality testing. In this paper, we investigate the effects of small error rates in a set of measurements or observations. We find that even with very low systemic failure rates, high confidence is surprisingly difficult to achieve; in particular, we find that certain analyses of cryptographically important numerical tests are highly optimistic, underestimating their false-negative rate by as much as a factor of 2^80 .
In this paper, we evaluate the encoding efficiency of suprathreshold stochastic resonance (SSR) b... more In this paper, we evaluate the encoding efficiency of suprathreshold stochastic resonance (SSR) based on a local information-theoretic measure of stimulus-specific information (SSI), which is the average specific information of responses associated with a particular stimulus. The theoretical and numerical analyses of SSIs reveal that noise can improve neuronal coding efficiency for a large population of neurons, which leads to produce increased information-rich responses. The SSI measure, in contrast to the global measure of average mutual information, can characterize the noise benefits in finer detail for describing the enhancement of neuronal encoding efficiency of a particular stimulus, which may be of general utility in the design and implementation of a SSR coding scheme.
Physica A: Statistical Mechanics and its Applications, 2008
We consider an isolated dynamical saturating system for processing a noisy sinusoidal signal, and... more We consider an isolated dynamical saturating system for processing a noisy sinusoidal signal, and evaluate its performance with the measure of the signal-to-noise ratio. The considered system is linear for small inputs, but exhibits saturation in its response for large inputs. This nonlinearity displays the nonlinear phenomenon of stochastic resonance for a large biased sinusoid in appropriate system parameter regions. Without the stochastic resonance phenomenon, this dynamical saturating system can achieve a signalto-noise ratio gain exceeding unity for a noisy unbiased sinusoid. These numerical results manifest the nonlinearities and the signal-processing ability of this system acting as a stochastic resonator or a signal processor.
Noise-enhanced transmission efficacy of aperiodic signals in nonlinear systems
International Journal of Modern Physics: Conference Series, 2014
ABSTRACT We study the aperiodic signal transmission in a static nonlinearity in the context of ap... more ABSTRACT We study the aperiodic signal transmission in a static nonlinearity in the context of aperiodic stochastic resonance. The performance of a nonlinearity over that of the lin-ear system is defined as the transmission efficacy. The theoretical and numerical results demonstrate that the noise-enhanced transmission efficacy effects occur for different sig-nal strengths in various noise scenarios.
Physics Letters A, 2014
In an ad hoc suboptimal detector, the benefits of non-Gaussian noise to narrowband weak signal de... more In an ad hoc suboptimal detector, the benefits of non-Gaussian noise to narrowband weak signal detection are demonstrated. Particularly, for a noise envelope with a Rice distribution, we can improve the detector performance by tuning threshold parameter but keeping noise level, or increasing the noise level for a fixed threshold. It is verified that, under certain circumstances, the optimal detection probability achieved by tuning noise level is superior to that obtained by optimizing the detector threshold.
Neurocomputing, 2007
A classic model neuron with threshold and saturation is used to form parallel uncoupled neuronal ... more A classic model neuron with threshold and saturation is used to form parallel uncoupled neuronal arrays in charge of the transduction of a periodic or aperiodic noisy input signal. The impact on the transduction efficacy of added noises is investigated. In isolated neurons, improvement by noise is possible only in the subthreshold and in the strongly saturating regimes of the neuronal response. In arrays, improvement by noise is always reinforced, and it becomes possible in all regimes of operation, i.e. in the threshold, in the saturation, and also in the intermediate curvilinear part of the neuronal response. All the configurations of improvement by noise apply equally to periodic and to aperiodic signals. These results extend the possible forms of stochastic resonance or improvement by noise accessible in neuronal systems for the processing of information. r
Lecture Notes in Computer Science, 2008
The pair correlation integral is used to assess the intrinsic dimensionality of the three-dimensi... more The pair correlation integral is used to assess the intrinsic dimensionality of the three-dimensional histogram of RGB color images. For application in the bounded colorimetric cube, this correlation measure is first calibrated on color histograms of reference constructed with integer dimensionality. The measure is then applied to natural color images. The results show that their color histogram tends to display a self-similar structure with noninteger fractal dimension. Such a fractal organization in the colorimetric space can have relevance for image segmentation or classification, or other areas of color image processing.
DYNAMIC PROPERTIES OF A BIOLOGICALLY MOTIVATED NEURAL NETWORK MODEL
International Journal of Neural Systems, 1992
ABSTRACT
Physical review. E, Statistical, nonlinear, and soft matter physics, 2003
We analyze the parametric estimation that can be performed on a signal buried in noise based on t... more We analyze the parametric estimation that can be performed on a signal buried in noise based on the parsimonious representation provided by a parallel array of threshold devices. The Fisher information contained in the array output about the input parameter is used as the measure of performance in the estimation task. For estimation on a suprathreshold input signal, we establish that enhancement of the Fisher information can be obtained by addition of independent noises to the thresholds in the array. Similar improvement by noise is also shown to be possible for the estimation error of the maximum likelihood estimator. These results extend the applicability of the recently introduced nonlinear phenomenon of suprathreshold stochastic resonance.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
This paper studies the signal-to-noise ratio (SNR) gain of a parallel array of nonlinear elements... more This paper studies the signal-to-noise ratio (SNR) gain of a parallel array of nonlinear elements that transmits a common input composed of a periodic signal and external noise. Aiming to further enhance the SNR gain, each element is injected with internal noise components or high-frequency sinusoidal vibrations. We report that the SNR gain exhibits two maxima at different values of the internal noise level or of the sinusoidal vibration amplitude. For the addition of internal noise to an array of threshold-based elements, the condition for occurrence of stochastic resonance is analytically investigated in the limit of weak signals. Interestingly, when the internal noise components are replaced by high-frequency sinusoidal vibrations, the SNR gain displays the vibrational multiresonance phenomenon. In both considered cases, there are certain regions of the internal noise intensity or the sinusoidal vibration amplitude wherein the achieved maximal SNR gain can be considerably beyond ...
PloS one, 2012
The origins of Fisher information are in its use as a performance measure for parametric estimati... more The origins of Fisher information are in its use as a performance measure for parametric estimation. We augment this and show that the Fisher information can characterize the performance in several other significant signal processing operations. For processing of a weak signal in additive white noise, we demonstrate that the Fisher information determines (i) the maximum output signal-to-noise ratio for a periodic signal; (ii) the optimum asymptotic efficacy for signal detection; (iii) the best cross-correlation coefficient for signal transmission; and (iv) the minimum mean square error of an unbiased estimator. This unifying picture, via inequalities on the Fisher information, is used to establish conditions where improvement by noise through stochastic resonance is feasible or not.
Enhancement by noise in parallel arrays of sensors with power-law characteristics
Physical review. E, Statistical, nonlinear, and soft matter physics, 2004
An optimally tuned power-law sensor is shown capable of amplifying the signal-to-noise ratio of a... more An optimally tuned power-law sensor is shown capable of amplifying the signal-to-noise ratio of a sine wave in Gaussian white noise. When associated in parallel arrays, further improvement can be obtained with independent noises injected on these sensors. This form of stochastic resonance in arrays, obtained here with smooth threshold-free nonlinearities, yields signal-to-noise ratio gains above unity in a true regime of added noise for a sine wave in Gaussian white noise, along with a class of nonlinear devices with useful potentialities for noise-aided information processing.
Rényi entropy measure of noise-aided information transmission in a binary channel
Physical review. E, Statistical, nonlinear, and soft matter physics, 2010
This paper analyzes a binary channel by means of information measures based on the Rényi entropy.... more This paper analyzes a binary channel by means of information measures based on the Rényi entropy. The analysis extends, and contains as a special case, the classic reference model of binary information transmission based on the Shannon entropy measure. The extended model is used to investigate further possibilities and properties of stochastic resonance or noise-aided information transmission. The results demonstrate that stochastic resonance occurs in the information channel and is registered by the Rényi entropy measures at any finite order, including the Shannon order. Furthermore, in definite conditions, when seeking the Rényi information measures that best exploit stochastic resonance, then nontrivial orders differing from the Shannon case usually emerge. In this way, through binary information transmission, stochastic resonance identifies optimal Rényi measures of information differing from the classic Shannon measure. A confrontation of the quantitative information measures w...
Computer vision under inactinic light for hypocotyl–radicle separation with a generic gravitropism-based criterion
Computers and Electronics in Agriculture, 2015
ABSTRACT This article proposes a computer-vision based protocol, useful to contribute to high-thr... more ABSTRACT This article proposes a computer-vision based protocol, useful to contribute to high-throughput automated phenotyping of seedlings during elongation, the stage following germination. Radicle and hypocotyl are two essential organs which start to develop at this stage, with the hypocotyl growing towards the soil surface and the radicle exploring deeper layers for nutrient absorption. Early identification and measurement of these two organs are important to the characterization of the plant emergence and to the prognosis of the adult plant. In normal conditions, this growth process of radicle and hypocotyl takes place in the soil, in the dark. Identification and measurement of these two organs are therefore challenging, because they need to be achieved with no light that could alter normal growth conditions. We propose here an original protocol exploiting an inactinic green light, produced by a controlled LED source, coupled to a standard low-cost gray-level camera. On the resulting digital images, we devise a simple criterion based on gravitropism and amenable to direct computer implementation. The automated criterion, through comparison with the performance of human experts, is demonstrated to be efficient for the detection and separation of radicle and hypocotyl, and generic for various species of seedlings. Our protocol especially brings improvement in terms of cost reduction over the current method found in the recent literature which resorts to higher-cost passive thermal imaging to perform the same task in the dark, and that we also consider here for comparison. Our protocol connected to automation of image acquisition, can serve to improve high-throughput phenotyping equipments for analysis of seed quality and genetic variability.
Fundamentals and Applications, 2014
In imaging, the choice of an observation scale is conventionally settled by the operator in charg... more In imaging, the choice of an observation scale is conventionally settled by the operator in charge of the image acquisition, who is left alone with tuning the framing and zooming parameters of the imaging system. In a somewhat decoupled manner, the operator in charge of processing the data has access to the images after their acquisition, and seeks to extract information from the observed scene. This Letter proposes a manifestation of the interest of an alternative joint acquisition-processing approach. We demonstrate with quantitative informational measures how the choice of an observation scale can be directly related to the performance of the final information processing task. Illustrations are given with various tools from statistical information theory with possible applications of practical interest to any noisy imaging domains.
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Papers by François Chapeau-Blondeau