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The performance capability of quadratic Hebbian type associative memories (QHAM's) in the presence of interconnection faults is examined, and equations for predicting the probability of direct convergence P(dc) given a fraction of interconnection faults are developed. The interconnection faults considered are the equivalent of open circuit and short circuit synaptic interconnections in electronic implementations. Our results show that a network with open circuit interconnection faults has a higher probability of direct convergence P (dc) than a network with short circuit interconnection faults, when the fraction of failed interconnections p is small and the short circuit signal G is large. Certain values of G are found to have only mild effects on network performance degradation. Network reliability characteristics taking the generalization capability into account are also analyzed. All of these results are compared with those of Hebbian type associative memories (HAM's), which have linear association network models. Our results indicate that QHAM's have much higher network capacity and fault tolerance capability in the presence of interconnection faults. However, the fault tolerance to input errors in QHAM's is much less than that of HAM's.
RESUMEN
The performance of Hebbian-type associative memories (HAMs) in the presence of faulty (open- and short-circuit) synaptic interconnections is examined and equations for predicting network reliability are developed. The results show that a network with open-circuit interconnection faults has a higher probability of direct convergence than a network with short-circuit interconnection faults when the fraction of failed interconnections is small and the short-circuit signal is large. The results are extended to the case where network attraction radius is considered. Under certain assumptions, it is found that the expected numbers of neurons with b, b-1, b-2,. . .,1 input error bits in their state update are equal. Because of the capability of error correction, an asynchronous HAM is also found to have a higher probability of direct convergence than a synchronous HAM. Using these results, network reliability and generalization capability can be estimated when both the interconnection faults and the number of error bits in the probe vectors are taken into account.
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The power cepstrum (power spectrum of the log of the power spectrum) of a signal in a multipath environment provides information on echo amplitudes and delay times. An electrooptical power cepstrum analyzer, which displays this information in real time, is described. The basic system approach is to use optics to provide the power spectrums and electronics to provide the logarithm function. The design and experimental results of a working system are presented.
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System theory for holographic representation of linear space-variant systems is derived. The utility of the resulting piecewise isoplanatic approximation (PIA) is illustrated by example application to the invariant system, ideal magnifier, and Fourier transformer. A method previously employed to holographically represent a space-variant system, the discrete approximation, is shown to be a special case of the PIA.
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Several techniques for the holographic representation of any bandlimited space-variant system by spatially sampling the input plane and multiplexing the respective system transfer functions have been previously described. This paper describes an alternative multiplexing technique in which the transfer functions are sampled in the Fourier plane to produce the multiplexed holograms. Various techniques for generating multiple copies of the input function that are required during playback are considered. Experimental results using computer-multiplexed holograms are also presented.
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Optimal estimators are derived for a signal-dependent film-grain noise model, and the effect of signal-dependence on the estimators's structures is investigated. Due to the mathematical complexity of these optimal estimators, various suboptimal estimators are proposed. Computer simulations are then presented which compare the optimal and suboptimal estimators with regard to mean square estimation error, sensitivity to signal-dependence, and robustness with respect to the a priori signal probability density function.
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The performance of an image compression scheme is affected by the presence of noise, and the achievable compression may be reduced significantly. We investigated the effects of specific signal-dependent-noise (SDN) sources, such as film-grain and speckle noise, on image compression, using JPEG (Joint Photographic Experts Group) standard image compression. For the improvement of compression ratios noisy images are preprocessed for noise suppression before compression is applied. Two approaches are employed for noise suppression. In one approach an estimator designed specifically for the SDN model is used. In an alternate approach, the noise is first transformed into signal-independent noise (SIN) and then an estimator designed for SIN is employed. The performances of these two schemes are compared. The compression results achieved for noiseless, noisy, and restored images are also presented.
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We investigate the temporal intensity noise characteristics of analog liquid-crystal-based spatial light modulators and how they affect the device's achievable discrete numeric accuracies in an optical computing system. First we present an analytical development that defines the concept of precision in analog computing systems, then we define a noise metric and a precision-optimal quantizer for determining the discrete numeric characteristics of the devices. Second we present an experimental discussion in which a low-noise test facility constructed for this investigation is described, and the noise characteristics of three commercially available liquid-crystal-based modulators are measured and analyzed. The accuracy implications of this measured noise are then discussed within the context of the analytical model for each modulator.
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Digital partitioning and error-correcting codes provide a technique for achieving high-accuracy computations with analog optical matrix-vector processors. We present the results of a detailed throughput analysis of this technique. The results indicate that using one processor per submatrix provides the best compromise between system throughput and hardware requirements over a range of matrix sizes. Errorcorrecting codes are shown to not significantly degrade system throughput for large matrix sizes. Finally, a comparison to digital electronic computers is made.
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The use of power cepstrum analysis in image registration is explored. Rotational shifts and translational shifts are corrected separately. The technique involves two main ideas. First, after preprocessing to remove extraneous information and information which could result in false registration parameters, a rotational shift is changed into a translational shift by using the shift-invariant property of the power spectrum. Second, power cepstrum analysis is used to correct the translational shift. Because of the introduction of these ideas, this new algorithm can work very fast and accurately compared to conventional correlation techniques. This registration technique is applied to sequential fundus images with potential application in detecting changes in fundus anomalies.
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A 2-D optical three-stage Clos interconnection network, which is made up of a number of feasible crossbars of medium size, is implemented for dynamic data communications. The network is nonblocking and can handle a large number of communication lines (compared with crossbar networks of realizable size). Doth one-to-one and one-to-many routing algorithms are discussed. Applications based on the Clos network are proposed for SIMD (single instruction multiple data) parallel computations and four-level programmable logic arrays (PLAs).
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Error-correcting codes provide a technique for enhancing the accuracy of optical matrix-vector multipliers (OMVM's). The effects of signal-independent and signal-dependent noise on the performance of OMVM's that employ error-correcting codes are studied through the use of computer simulations. Noise present in the matrix results in random errors that can be corrected by these codes. Noise present in the vector results in nonrandom errors that are difficult to correct by using random error-correcting codes. The effect of code type is also investigated.
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A transformation to convert signal-dependent noise corrupting an image to additive Gaussian signal-independent noise is derived in this paper. Wiener filtering techniques using a Markovian covariance model for the image signal are applied to the transformed data followed by an inverse transformation to restore the degraded image. An ad hoc technique using contrast manipulation to adaptively convert signal-dependent noise to signal-independent noise is also described. The results of the computer simulations designed to evaluate the performance of these techniques are also presented.
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It is well known that the noise processes corrupting an image are, in general, signal dependent. Under low signal to-noise-ratio situations, the amount of signal information present in the signal-dependent noise may become a significant fraction of the total signal information. A simple technique designed to demonstrate the potential for signal extraction from signal-dependent noise is presented.
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Two general schemes for 1-D space-variant processing are proposed. The direct output display scheme gives the space-variant system output along a line in the processor's output plane. The output spectrum display scheme directly computes the space-variant system's output spectrum. Both of these schemes utilize a 1-D input and a line spread function mask. Example applications and experimental results are also presented.
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A coherent optical processor for displaying a signal's ambiguity function is described. The required time delay is realized by 45 degrees rotations of two identical input transparencies and the Doppler shift by a 1-D Fourier transformation. The entire ambiguity function is displayed in the output (Doppler shift-time delay) plane. Examples of the optically computed ambiguity function for single and double pulse signals are shown to be in excellent agreement with theory. Advantages of this approach over other schemes and possible extension to real time processing are also discussed.
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A new holographic implementation of a sampling technique permits, in principle, a straightforward representation of 2-D space-variant optical systems. The set of sample transfer functions required for the representation is recorded on a single holographic plate by utilizing phase coded reference beams. Because this approach does not depend on volume effects in the recording medium in an essential way, the holograms can be produced digitally, as well as optically. Basic concepts and preliminary experimental investigations related to this approach are presented and discussed.
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Certain binary codes developed for spread-spectrum communication applications can be used to construct families of pseudorandom diffuser masks suitable for multiplex holography. Binary codes are used so that fabrication of the diffuser masks can be relatively straightforward. A simple technique is described for chirp-modulating the binary diffuser masks to achieve the advantage of polyphase masks, i.e., improved correlation properties, without having to construct them. Numerical comparisons of the correlation properties of optimal binary codes with and without chirp-modulation are presented.
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The capacity to use differing read and write wavelengths for reconstructing volume holograms recorded in a shift-multiplexing geometry is analyzed and realized for M-type volume holograms recorded on bacteriorhodopsin films. The intensity distribution in the reconstructed wave is calculated as a function of the parameters of the recording and readout beams. Optimal recording and retrieving geometries, as well as a precise method for tuning the readout setup, are suggested.
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We present a multiple-input, single-output, weakly nonlinear model of spatial light modulators by use of a second-order Volterra series and describe an experimental method to measure the nonlinear transfer functions by means of sinusoidal perturbation and synchronous detection with a lock-in amplifier. We also present an application of this method to a liquid-crystal light valve.