A theory is presented addressing the fundamental limits of image estimation in a setup that uses two photon-correlated beams. These beams have the property that their photon arrivals, as a point process, are ideally synchronized in time and space. The true image represents the spatial distribution of the optical transmittance (or reflectance) of an object. In this setup, one beam is used to probe the image while the other is used as a reference providing additional information on the actual number of photons impinging on the object. This additional information is exploited to reduce the effect of quantum noise associated with the uncertainty in the number of photons per pixel. A stochastic model for the joint statistics of the two observation matrices is developed and used to obtain a local maximum-likelihood estimator of the image. The model captures the nonideal nature of the correlation between the photons of the beams by means of a simple random translation model. The mean-square error of the estimator is evaluated and compared to the corresponding conventional techniques. Conditions for the performance advantage of the proposed estimator are examined in terms of key system parameters. The theoretical predictions are demonstrated by means of simulation.

The performance of neural networks for which weights and signals are modeled by shot-noise processes is considered. Examples of such networks are optical neural networks and biological systems. We develop a theory that facilitates the computation of the average probability of error in binary-input/binary-output multistage and recurrent networks. We express the probability of error in terms of two key parameters: the computing-noise parameter and the weight-recording-noise parameter. The former is the average number of particles per clock cycle per signal and it represents noise due to the particle nature of the signal. The latter represents noise in the weight-recording process and is the average number of particles per weight. For a fixed computing-noise parameter, the probability of error decreases with the increase in the recording-noise parameter and saturates at a level limited by the computing-noise parameter. A similar behavior is observed when the role of the two parameters is interchanged. As both parameters increase, the probability of error decreases to zero exponentially fast at a rate that is determined using large deviations. We show that the performance can be optimized by a selective choice of the nonlinearity threshold levels. For recurrent networks, as the number of iterations increases, the probability of error increases initially and then saturates at a level determined by the stationary distribution of a Markov chain.

Bit-error rates are computed for an on-off keying optical communication system using avalanche photodiodes (APDs). We use a model for the APD that includes dead space and the finite response time. Dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing an impact ionization in the multiplication region of the APD. The detector's finite impulse response and its randomness are important for high data-rate systems. Using an exact analysis, we show that the presence of dead space enhances the performance at relatively low data rates. Using a Gaussian approximation technique with the exact mean and variance, we demonstrate that dead space degrades the performance at-high data rates since it is responsible for longer tails in the impulse response function of the APD, which in turn increases the effect of intersymbol interference.>

Images that are to be transmitted through a distorting imaging system may be deliberately altered to compensate for that distortion. The authors consider an incoherent diffraction-limited imaging system followed by an ideal high-contrast detector that prints binary images, and seek a binary input image (a mask) that generates a desired prescribed binary output image. They have developed a method for determining the optimal binary mask by formulating the problem as a mixed linear integer program (MLIP) and using the branch and bound method to solve it.

Image detection under low-light-level conditions is treated as a hypothesis-testing problem in which the observations are modeled as a shot-noise process. Since computing the likelihood ratio for shot-noise processes is not feasible, the use of a one-dimensional test statistic obtained by filtering and sampling the observations is proposed. The filter is chosen to maximize a generalized signal-to-noise ratio. The likelihood ratio for the one-dimensional test statistic is evaluated numerically by inverting the corresponding characteristic function under each hypothesis.

Several methods have been proposed for the generation of photon-number-squeezed (sub-Poisson) light by imparting to the photon stream and anticorrelation that regularizes the times of arrival of the photons. This is accomplished by means of control of the excitation or emission process or by feedback, using a copy of the photon point processes when the emissions occur in parts. Possible advantages of communication by photon-number-squeezed light are discussed. For receivers in which the photon arrival times are observed, the channel capacity cannot be improved by modifying an initially Poisson photon stream and making it sub-Poisson. For photon-counting receivers, however, improvement of the channel capacity is possible. The bit-error-rate of an on-off keying communication system using sub-Poisson photons created by introducing anticorrelation into an initially Poisson beam may or may not be smaller than the error rates of the Poisson channel, depending on where the maximum power constraint is placed.>

A method is introduced for finding a signal f(n) with a time-varying spectrum C(n omega ) approximating a geometric transformation C( alpha n, beta omega ) in the mean-square sense. The phases of C(n, omega ) and C( alpha n, beta omega ) are allowed to differ by a smooth function of n and omega selected to minimize the overall difference between these complex functions. The result is a periodically time-varying filter relating f(n) and f(n), which is easy to implement, requiring few arithmetic operations per output sample. The method shows high fidelity in recovering the original signal from its scaled version. It is shown that for the same bit rate reduction, joint time-frequency scaling renders higher signal-to-noise ratios than either time-only or frequency-only scaling.>

The authors present a new method for time scaling of speech signals based on scaling the short-time Fourier transform (STFT) along the time axis while keeping it unchanged along the frequency axis. Because the resultant time-frequency function is not an admissible STFT, they project it on the space of admissible STFTs, i.e., they find a signal whose STFT best approximates the time-frequency function. The time-scaled signal is related to the original signal by a linear periodically-time-varying filter, which is simple to implement. High quality time-scaled words and sentences have been obtained using this method.>

A multiplicative gain control mechanism to account for the gradual fading of a stabilized image, the off-image, and the phenomenon of apparent contrast reversal is proposed. This phenomenon occurs when a uniform increment is added to a fading image. Fading and time-to-disappearance are examined as functions of contrast, spatial frequency, and average luminance. Contrast threshold for off-images is also derived. Predictions of the model are compared to data when available. It is shown that this multiplicative model predicts a recent observation that the difference between contrast "thresholds" under stabilized and unstabilized conditions is equal to the contrast of the off-image produced by a stimulus whose contrast equals the stabilized contrast "threshold." An additive model is also investigated and shown to be incapable of accounting for some of the phenomena.

Image design involves determining the object distribution which produces a prescribed image at the output of a given imaging system. We solve the problem of generating two parallel lines at the output of an imaging system that is modeled by a linear band-limited system foliowed by a point nonlinearity of the hardlimiting type. It is shown that a solution always exists whatever the system's bandwidth. In principle, infinite two-line resolution is achievable. In practice, resolution much higher than the conventional resolution of the imaging system is possible.

A recurrence relation is obtained for the counting distribution, as well as the probability density of waiting time, for a doubly stochastic Poisson point process driven by nonstationary shot noise (SNDP). For a stimulus of short duration, the counting distribution approximately reduces to the Neyman Type-A. The SNDP is an important special Neyman-Scott cluster process.

The effect of retinal spatial interactions on photon-fluctuation noise is studied. We show that lateral inhibition results in an increase of the susceptibility to that noise, whereas spatial summations result in the opposite. We present a quantitative assessment of the adaptive changes in the form of the receptive field that should accompany changes in luminance, in order to achieve an optimum trade-off between resolution and noise.

A simple relation is found between the probability distribution of time of arrival of photoevents and the moment-generating function of the detected optical energy of a general stationary optical field. This is applied to the case of a Gaussian-Lorentzian field and the case of a mixture of coherent and thermal light.